Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [32,4,Mod(5,32)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(32, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("32.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 32 = 2^{5} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 32.g (of order \(8\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.88806112018\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 5.8 | ||
Character | \(\chi\) | \(=\) | 32.5 |
Dual form | 32.4.g.a.13.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/32\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(31\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.49948 | − | 2.39824i | 0.530146 | − | 0.847906i | ||||
\(3\) | 2.92731 | + | 7.06715i | 0.563361 | + | 1.36007i | 0.907063 | + | 0.420995i | \(0.138319\pi\) |
−0.343702 | + | 0.939079i | \(0.611681\pi\) | |||||||
\(4\) | −3.50313 | − | 7.19223i | −0.437891 | − | 0.899028i | ||||
\(5\) | 13.5234 | + | 5.60159i | 1.20957 | + | 0.501022i | 0.894081 | − | 0.447906i | \(-0.147830\pi\) |
0.315493 | + | 0.948928i | \(0.397830\pi\) | |||||||
\(6\) | 21.3382 | + | 3.57665i | 1.45188 | + | 0.243360i | ||||
\(7\) | −23.0737 | − | 23.0737i | −1.24586 | − | 1.24586i | −0.957530 | − | 0.288335i | \(-0.906898\pi\) |
−0.288335 | − | 0.957530i | \(-0.593102\pi\) | |||||||
\(8\) | −22.5016 | − | 2.38325i | −0.994438 | − | 0.105326i | ||||
\(9\) | −22.2836 | + | 22.2836i | −0.825318 | + | 0.825318i | ||||
\(10\) | 33.7121 | − | 24.0330i | 1.06607 | − | 0.759990i | ||||
\(11\) | −7.41078 | + | 17.8912i | −0.203130 | + | 0.490400i | −0.992312 | − | 0.123760i | \(-0.960505\pi\) |
0.789182 | + | 0.614159i | \(0.210505\pi\) | |||||||
\(12\) | 40.5738 | − | 45.8110i | 0.976054 | − | 1.10204i | ||||
\(13\) | 14.8121 | − | 6.13537i | 0.316010 | − | 0.130896i | −0.219040 | − | 0.975716i | \(-0.570293\pi\) |
0.535051 | + | 0.844820i | \(0.320293\pi\) | |||||||
\(14\) | −89.9350 | + | 20.7378i | −1.71687 | + | 0.395887i | ||||
\(15\) | 111.970i | 1.92737i | ||||||||
\(16\) | −39.4562 | + | 50.3905i | −0.616504 | + | 0.787352i | ||||
\(17\) | − | 27.7996i | − | 0.396611i | −0.980140 | − | 0.198305i | \(-0.936456\pi\) | ||
0.980140 | − | 0.198305i | \(-0.0635438\pi\) | |||||||
\(18\) | 20.0277 | + | 86.8552i | 0.262254 | + | 1.13733i | ||||
\(19\) | −82.2959 | + | 34.0881i | −0.993683 | + | 0.411597i | −0.819477 | − | 0.573112i | \(-0.805736\pi\) |
−0.174206 | + | 0.984709i | \(0.555736\pi\) | |||||||
\(20\) | −7.08639 | − | 116.887i | −0.0792283 | − | 1.30683i | ||||
\(21\) | 95.5216 | − | 230.610i | 0.992596 | − | 2.39634i | ||||
\(22\) | 31.7951 | + | 44.6003i | 0.308125 | + | 0.432219i | ||||
\(23\) | 39.2456 | − | 39.2456i | 0.355795 | − | 0.355795i | −0.506466 | − | 0.862260i | \(-0.669048\pi\) |
0.862260 | + | 0.506466i | \(0.169048\pi\) | |||||||
\(24\) | −49.0262 | − | 165.998i | −0.416977 | − | 1.41185i | ||||
\(25\) | 63.1173 | + | 63.1173i | 0.504938 | + | 0.504938i | ||||
\(26\) | 7.49632 | − | 44.7228i | 0.0565442 | − | 0.337341i | ||||
\(27\) | −31.8994 | − | 13.2132i | −0.227372 | − | 0.0941805i | ||||
\(28\) | −85.1213 | + | 246.782i | −0.574515 | + | 1.66562i | ||||
\(29\) | 5.57538 | + | 13.4602i | 0.0357008 | + | 0.0861892i | 0.940724 | − | 0.339172i | \(-0.110147\pi\) |
−0.905024 | + | 0.425362i | \(0.860147\pi\) | |||||||
\(30\) | 268.531 | + | 167.896i | 1.63423 | + | 1.02178i | ||||
\(31\) | 155.853 | 0.902970 | 0.451485 | − | 0.892279i | \(-0.350894\pi\) | ||||
0.451485 | + | 0.892279i | \(0.350894\pi\) | |||||||
\(32\) | 61.6849 | + | 170.185i | 0.340764 | + | 0.940149i | ||||
\(33\) | −148.133 | −0.781416 | ||||||||
\(34\) | −66.6701 | − | 41.6849i | −0.336289 | − | 0.210262i | ||||
\(35\) | −182.787 | − | 441.286i | −0.882760 | − | 2.13117i | ||||
\(36\) | 238.331 | + | 82.2064i | 1.10338 | + | 0.380585i | ||||
\(37\) | 188.743 | + | 78.1798i | 0.838625 | + | 0.347370i | 0.760311 | − | 0.649559i | \(-0.225046\pi\) |
0.0783139 | + | 0.996929i | \(0.475046\pi\) | |||||||
\(38\) | −41.6495 | + | 248.480i | −0.177801 | + | 1.06076i | ||||
\(39\) | 86.7192 | + | 86.7192i | 0.356056 | + | 0.356056i | ||||
\(40\) | −290.949 | − | 158.274i | −1.15007 | − | 0.625634i | ||||
\(41\) | 113.814 | − | 113.814i | 0.433530 | − | 0.433530i | −0.456297 | − | 0.889827i | \(-0.650825\pi\) |
0.889827 | + | 0.456297i | \(0.150825\pi\) | |||||||
\(42\) | −409.825 | − | 574.878i | −1.50565 | − | 2.11204i | ||||
\(43\) | −24.6509 | + | 59.5126i | −0.0874240 | + | 0.211060i | −0.961545 | − | 0.274649i | \(-0.911438\pi\) |
0.874121 | + | 0.485709i | \(0.161438\pi\) | |||||||
\(44\) | 154.638 | − | 9.37513i | 0.529832 | − | 0.0321217i | ||||
\(45\) | −426.174 | + | 176.527i | −1.41179 | + | 0.584781i | ||||
\(46\) | −35.2725 | − | 152.968i | −0.113058 | − | 0.490304i | ||||
\(47\) | 217.464i | 0.674902i | 0.941343 | + | 0.337451i | \(0.109565\pi\) | ||||
−0.941343 | + | 0.337451i | \(0.890435\pi\) | |||||||
\(48\) | −471.618 | − | 131.334i | −1.41817 | − | 0.394927i | ||||
\(49\) | 721.795i | 2.10436i | ||||||||
\(50\) | 246.014 | − | 56.7275i | 0.695831 | − | 0.160449i | ||||
\(51\) | 196.464 | − | 81.3779i | 0.539420 | − | 0.223435i | ||||
\(52\) | −96.0156 | − | 85.0390i | −0.256057 | − | 0.226784i | ||||
\(53\) | −35.7808 | + | 86.3826i | −0.0927335 | + | 0.223879i | −0.963440 | − | 0.267925i | \(-0.913662\pi\) |
0.870706 | + | 0.491803i | \(0.163662\pi\) | |||||||
\(54\) | −79.5208 | + | 56.6896i | −0.200397 | + | 0.142861i | ||||
\(55\) | −200.438 | + | 200.438i | −0.491402 | + | 0.491402i | ||||
\(56\) | 464.205 | + | 574.186i | 1.10771 | + | 1.37016i | ||||
\(57\) | −481.811 | − | 481.811i | −1.11960 | − | 1.11960i | ||||
\(58\) | 40.6409 | + | 6.81211i | 0.0920070 | + | 0.0154220i | ||||
\(59\) | −116.586 | − | 48.2914i | −0.257257 | − | 0.106559i | 0.250328 | − | 0.968161i | \(-0.419462\pi\) |
−0.507585 | + | 0.861602i | \(0.669462\pi\) | |||||||
\(60\) | 805.312 | − | 392.244i | 1.73276 | − | 0.843975i | ||||
\(61\) | −197.015 | − | 475.636i | −0.413528 | − | 0.998344i | −0.984183 | − | 0.177155i | \(-0.943311\pi\) |
0.570655 | − | 0.821190i | \(-0.306689\pi\) | |||||||
\(62\) | 233.699 | − | 373.774i | 0.478706 | − | 0.765634i | ||||
\(63\) | 1028.33 | 2.05647 | ||||||||
\(64\) | 500.640 | + | 107.254i | 0.977813 | + | 0.209480i | ||||
\(65\) | 234.678 | 0.447819 | ||||||||
\(66\) | −222.123 | + | 355.260i | −0.414264 | + | 0.662567i | ||||
\(67\) | 144.765 | + | 349.494i | 0.263968 | + | 0.637276i | 0.999177 | − | 0.0405648i | \(-0.0129157\pi\) |
−0.735208 | + | 0.677841i | \(0.762916\pi\) | |||||||
\(68\) | −199.941 | + | 97.3854i | −0.356564 | + | 0.173672i | ||||
\(69\) | 392.239 | + | 162.471i | 0.684348 | + | 0.283466i | ||||
\(70\) | −1332.40 | − | 223.333i | −2.27502 | − | 0.381334i | ||||
\(71\) | −523.475 | − | 523.475i | −0.875001 | − | 0.875001i | 0.118011 | − | 0.993012i | \(-0.462348\pi\) |
−0.993012 | + | 0.118011i | \(0.962348\pi\) | |||||||
\(72\) | 554.523 | − | 448.308i | 0.907655 | − | 0.733800i | ||||
\(73\) | −718.521 | + | 718.521i | −1.15201 | + | 1.15201i | −0.165856 | + | 0.986150i | \(0.553039\pi\) |
−0.986150 | + | 0.165856i | \(0.946961\pi\) | |||||||
\(74\) | 470.510 | − | 335.422i | 0.739131 | − | 0.526919i | ||||
\(75\) | −261.296 | + | 630.823i | −0.402291 | + | 0.971216i | ||||
\(76\) | 533.462 | + | 472.476i | 0.805162 | + | 0.713115i | ||||
\(77\) | 583.811 | − | 241.822i | 0.864045 | − | 0.357899i | ||||
\(78\) | 338.007 | − | 77.9399i | 0.490664 | − | 0.113141i | ||||
\(79\) | − | 958.779i | − | 1.36546i | −0.730673 | − | 0.682728i | \(-0.760793\pi\) | ||
0.730673 | − | 0.682728i | \(-0.239207\pi\) | |||||||
\(80\) | −815.851 | + | 460.436i | −1.14019 | + | 0.643479i | ||||
\(81\) | 586.755i | 0.804876i | ||||||||
\(82\) | −102.292 | − | 443.614i | −0.137759 | − | 0.597427i | ||||
\(83\) | 1241.90 | − | 514.414i | 1.64237 | − | 0.680292i | 0.645836 | − | 0.763476i | \(-0.276509\pi\) |
0.996534 | + | 0.0831842i | \(0.0265090\pi\) | |||||||
\(84\) | −1993.22 | + | 120.841i | −2.58903 | + | 0.156963i | ||||
\(85\) | 155.722 | − | 375.946i | 0.198711 | − | 0.479730i | ||||
\(86\) | 105.762 | + | 148.357i | 0.132612 | + | 0.186020i | ||||
\(87\) | −78.8041 | + | 78.8041i | −0.0971113 | + | 0.0971113i | ||||
\(88\) | 209.393 | − | 384.918i | 0.253652 | − | 0.466277i | ||||
\(89\) | −808.016 | − | 808.016i | −0.962354 | − | 0.962354i | 0.0369622 | − | 0.999317i | \(-0.488232\pi\) |
−0.999317 | + | 0.0369622i | \(0.988232\pi\) | |||||||
\(90\) | −215.685 | + | 1286.77i | −0.252613 | + | 1.50708i | ||||
\(91\) | −483.336 | − | 200.204i | −0.556785 | − | 0.230628i | ||||
\(92\) | −419.746 | − | 144.781i | −0.475669 | − | 0.164070i | ||||
\(93\) | 456.231 | + | 1101.44i | 0.508698 | + | 1.22811i | ||||
\(94\) | 521.531 | + | 326.083i | 0.572253 | + | 0.357796i | ||||
\(95\) | −1303.87 | −1.40815 | ||||||||
\(96\) | −1022.15 | + | 934.121i | −1.08670 | + | 0.993108i | ||||
\(97\) | 1399.29 | 1.46471 | 0.732354 | − | 0.680924i | \(-0.238422\pi\) | ||||
0.732354 | + | 0.680924i | \(0.238422\pi\) | |||||||
\(98\) | 1731.04 | + | 1082.32i | 1.78430 | + | 1.11562i | ||||
\(99\) | −233.541 | − | 563.819i | −0.237089 | − | 0.572383i | ||||
\(100\) | 232.846 | − | 675.062i | 0.232846 | − | 0.675062i | ||||
\(101\) | −1024.11 | − | 424.200i | −1.00894 | − | 0.417916i | −0.183871 | − | 0.982950i | \(-0.558863\pi\) |
−0.825067 | + | 0.565035i | \(0.808863\pi\) | |||||||
\(102\) | 99.4293 | − | 593.192i | 0.0965193 | − | 0.575831i | ||||
\(103\) | −483.862 | − | 483.862i | −0.462877 | − | 0.462877i | 0.436720 | − | 0.899597i | \(-0.356140\pi\) |
−0.899597 | + | 0.436720i | \(0.856140\pi\) | |||||||
\(104\) | −347.917 | + | 102.754i | −0.328039 | + | 0.0968837i | ||||
\(105\) | 2583.56 | − | 2583.56i | 2.40124 | − | 2.40124i | ||||
\(106\) | 153.514 | + | 215.340i | 0.140666 | + | 0.197318i | ||||
\(107\) | −682.420 | + | 1647.51i | −0.616561 | + | 1.48851i | 0.239112 | + | 0.970992i | \(0.423144\pi\) |
−0.855673 | + | 0.517517i | \(0.826856\pi\) | |||||||
\(108\) | 16.7155 | + | 275.715i | 0.0148931 | + | 0.245655i | ||||
\(109\) | −1813.85 | + | 751.322i | −1.59390 | + | 0.660217i | −0.990537 | − | 0.137247i | \(-0.956175\pi\) |
−0.603367 | + | 0.797463i | \(0.706175\pi\) | |||||||
\(110\) | 180.147 | + | 781.253i | 0.156148 | + | 0.677178i | ||||
\(111\) | 1562.73i | 1.33629i | ||||||||
\(112\) | 2073.10 | − | 252.295i | 1.74901 | − | 0.212854i | ||||
\(113\) | − | 1392.34i | − | 1.15912i | −0.814931 | − | 0.579558i | \(-0.803225\pi\) | ||
0.814931 | − | 0.579558i | \(-0.196775\pi\) | |||||||
\(114\) | −1877.97 | + | 433.034i | −1.54287 | + | 0.355766i | ||||
\(115\) | 750.574 | − | 310.898i | 0.608621 | − | 0.252099i | ||||
\(116\) | 77.2772 | − | 87.2520i | 0.0618535 | − | 0.0698374i | ||||
\(117\) | −193.349 | + | 466.785i | −0.152778 | + | 0.368840i | ||||
\(118\) | −290.632 | + | 207.189i | −0.226736 | + | 0.161638i | ||||
\(119\) | −641.440 | + | 641.440i | −0.494123 | + | 0.494123i | ||||
\(120\) | 266.852 | − | 2519.49i | 0.203001 | − | 1.91664i | ||||
\(121\) | 675.984 | + | 675.984i | 0.507877 | + | 0.507877i | ||||
\(122\) | −1436.11 | − | 240.717i | −1.06573 | − | 0.178635i | ||||
\(123\) | 1137.51 | + | 471.171i | 0.833867 | + | 0.345399i | ||||
\(124\) | −545.974 | − | 1120.93i | −0.395402 | − | 0.811796i | ||||
\(125\) | −200.193 | − | 483.310i | −0.143247 | − | 0.345828i | ||||
\(126\) | 1541.96 | − | 2466.19i | 1.09023 | − | 1.74369i | ||||
\(127\) | 909.845 | 0.635714 | 0.317857 | − | 0.948139i | \(-0.397037\pi\) | ||||
0.317857 | + | 0.948139i | \(0.397037\pi\) | |||||||
\(128\) | 1007.92 | − | 1039.83i | 0.696003 | − | 0.718039i | ||||
\(129\) | −492.746 | −0.336309 | ||||||||
\(130\) | 351.895 | − | 562.815i | 0.237410 | − | 0.379709i | ||||
\(131\) | 375.465 | + | 906.452i | 0.250416 | + | 0.604558i | 0.998238 | − | 0.0593418i | \(-0.0189002\pi\) |
−0.747822 | + | 0.663900i | \(0.768900\pi\) | |||||||
\(132\) | 518.930 | + | 1065.41i | 0.342175 | + | 0.702515i | ||||
\(133\) | 2685.41 | + | 1112.34i | 1.75079 | + | 0.725201i | ||||
\(134\) | 1055.24 | + | 176.877i | 0.680292 | + | 0.114029i | ||||
\(135\) | −357.375 | − | 357.375i | −0.227837 | − | 0.227837i | ||||
\(136\) | −66.2533 | + | 625.534i | −0.0417734 | + | 0.394405i | ||||
\(137\) | −821.434 | + | 821.434i | −0.512262 | + | 0.512262i | −0.915219 | − | 0.402957i | \(-0.867982\pi\) |
0.402957 | + | 0.915219i | \(0.367982\pi\) | |||||||
\(138\) | 977.798 | − | 697.062i | 0.603157 | − | 0.429985i | ||||
\(139\) | 673.401 | − | 1625.73i | 0.410915 | − | 0.992036i | −0.573978 | − | 0.818871i | \(-0.694600\pi\) |
0.984893 | − | 0.173165i | \(-0.0553995\pi\) | |||||||
\(140\) | −2533.50 | + | 2860.52i | −1.52943 | + | 1.72685i | ||||
\(141\) | −1536.85 | + | 636.584i | −0.917916 | + | 0.380213i | ||||
\(142\) | −2040.36 | + | 470.480i | −1.20580 | + | 0.278041i | ||||
\(143\) | 310.474i | 0.181560i | ||||||||
\(144\) | −243.656 | − | 2002.11i | −0.141004 | − | 1.15863i | ||||
\(145\) | 213.259i | 0.122139i | ||||||||
\(146\) | 645.779 | + | 2800.59i | 0.366062 | + | 1.58753i | ||||
\(147\) | −5101.03 | + | 2112.92i | −2.86208 | + | 1.18551i | ||||
\(148\) | −98.9027 | − | 1631.36i | −0.0549308 | − | 0.906058i | ||||
\(149\) | 247.105 | − | 596.564i | 0.135863 | − | 0.328003i | −0.841275 | − | 0.540607i | \(-0.818195\pi\) |
0.977138 | + | 0.212604i | \(0.0681946\pi\) | |||||||
\(150\) | 1121.06 | + | 1572.56i | 0.610227 | + | 0.855991i | ||||
\(151\) | 373.703 | − | 373.703i | 0.201401 | − | 0.201401i | −0.599199 | − | 0.800600i | \(-0.704514\pi\) |
0.800600 | + | 0.599199i | \(0.204514\pi\) | |||||||
\(152\) | 1933.03 | − | 570.903i | 1.03151 | − | 0.304647i | ||||
\(153\) | 619.474 | + | 619.474i | 0.327330 | + | 0.327330i | ||||
\(154\) | 295.464 | − | 1762.73i | 0.154605 | − | 0.922368i | ||||
\(155\) | 2107.67 | + | 873.027i | 1.09221 | + | 0.452408i | ||||
\(156\) | 319.916 | − | 927.492i | 0.164191 | − | 0.476018i | ||||
\(157\) | −186.690 | − | 450.709i | −0.0949011 | − | 0.229112i | 0.869299 | − | 0.494286i | \(-0.164570\pi\) |
−0.964200 | + | 0.265174i | \(0.914570\pi\) | |||||||
\(158\) | −2299.38 | − | 1437.67i | −1.15778 | − | 0.723891i | ||||
\(159\) | −715.220 | −0.356734 | ||||||||
\(160\) | −119.116 | + | 2647.02i | −0.0588557 | + | 1.30791i | ||||
\(161\) | −1811.09 | −0.886544 | ||||||||
\(162\) | 1407.18 | + | 879.826i | 0.682460 | + | 0.426702i | ||||
\(163\) | −495.962 | − | 1197.36i | −0.238324 | − | 0.575364i | 0.758786 | − | 0.651340i | \(-0.225793\pi\) |
−0.997110 | + | 0.0759758i | \(0.975793\pi\) | |||||||
\(164\) | −1217.28 | − | 419.871i | −0.579595 | − | 0.199917i | ||||
\(165\) | −2003.27 | − | 829.783i | −0.945180 | − | 0.391506i | ||||
\(166\) | 628.521 | − | 3749.74i | 0.293872 | − | 1.75323i | ||||
\(167\) | −644.684 | − | 644.684i | −0.298725 | − | 0.298725i | 0.541789 | − | 0.840514i | \(-0.317747\pi\) |
−0.840514 | + | 0.541789i | \(0.817747\pi\) | |||||||
\(168\) | −2698.99 | + | 4961.42i | −1.23947 | + | 2.27846i | ||||
\(169\) | −1371.76 | + | 1371.76i | −0.624378 | + | 0.624378i | ||||
\(170\) | −668.107 | − | 937.181i | −0.301420 | − | 0.422815i | ||||
\(171\) | 1074.24 | − | 2593.45i | 0.480406 | − | 1.15980i | ||||
\(172\) | 514.384 | − | 31.1851i | 0.228031 | − | 0.0138247i | ||||
\(173\) | 2383.01 | − | 987.076i | 1.04727 | − | 0.433792i | 0.208351 | − | 0.978054i | \(-0.433190\pi\) |
0.838915 | + | 0.544262i | \(0.183190\pi\) | |||||||
\(174\) | 70.8262 | + | 307.156i | 0.0308581 | + | 0.133824i | ||||
\(175\) | − | 2912.70i | − | 1.25817i | ||||||
\(176\) | −609.146 | − | 1079.35i | −0.260887 | − | 0.462268i | ||||
\(177\) | − | 965.293i | − | 0.409920i | ||||||
\(178\) | −3149.42 | + | 726.215i | −1.32617 | + | 0.305798i | ||||
\(179\) | 3184.86 | − | 1319.21i | 1.32987 | − | 0.550852i | 0.399254 | − | 0.916840i | \(-0.369269\pi\) |
0.930619 | + | 0.365988i | \(0.119269\pi\) | |||||||
\(180\) | 2762.57 | + | 2446.75i | 1.14394 | + | 1.01316i | ||||
\(181\) | −820.433 | + | 1980.70i | −0.336919 | + | 0.813394i | 0.661089 | + | 0.750307i | \(0.270094\pi\) |
−0.998008 | + | 0.0630866i | \(0.979906\pi\) | |||||||
\(182\) | −1204.89 | + | 858.955i | −0.490728 | + | 0.349835i | ||||
\(183\) | 2784.67 | − | 2784.67i | 1.12486 | − | 1.12486i | ||||
\(184\) | −976.620 | + | 789.556i | −0.391290 | + | 0.316341i | ||||
\(185\) | 2114.52 | + | 2114.52i | 0.840339 | + | 0.840339i | ||||
\(186\) | 3325.62 | + | 557.432i | 1.31100 | + | 0.219747i | ||||
\(187\) | 497.368 | + | 206.016i | 0.194498 | + | 0.0805637i | ||||
\(188\) | 1564.05 | − | 761.803i | 0.606756 | − | 0.295533i | ||||
\(189\) | 431.161 | + | 1040.92i | 0.165938 | + | 0.400611i | ||||
\(190\) | −1955.13 | + | 3127.00i | −0.746526 | + | 1.19398i | ||||
\(191\) | −330.108 | −0.125056 | −0.0625282 | − | 0.998043i | \(-0.519916\pi\) | ||||
−0.0625282 | + | 0.998043i | \(0.519916\pi\) | |||||||
\(192\) | 707.551 | + | 3852.06i | 0.265954 | + | 1.44791i | ||||
\(193\) | −914.905 | −0.341224 | −0.170612 | − | 0.985338i | \(-0.554575\pi\) | ||||
−0.170612 | + | 0.985338i | \(0.554575\pi\) | |||||||
\(194\) | 2098.21 | − | 3355.84i | 0.776509 | − | 1.24194i | ||||
\(195\) | 686.976 | + | 1658.51i | 0.252284 | + | 0.609068i | ||||
\(196\) | 5191.31 | − | 2528.54i | 1.89188 | − | 0.921479i | ||||
\(197\) | −41.3093 | − | 17.1109i | −0.0149399 | − | 0.00618832i | 0.375201 | − | 0.926943i | \(-0.377574\pi\) |
−0.390141 | + | 0.920755i | \(0.627574\pi\) | |||||||
\(198\) | −1702.36 | − | 285.346i | −0.611019 | − | 0.102417i | ||||
\(199\) | 2946.98 | + | 2946.98i | 1.04978 | + | 1.04978i | 0.998694 | + | 0.0510831i | \(0.0162673\pi\) |
0.0510831 | + | 0.998694i | \(0.483733\pi\) | |||||||
\(200\) | −1269.81 | − | 1570.66i | −0.448947 | − | 0.555313i | ||||
\(201\) | −2046.16 | + | 2046.16i | −0.718033 | + | 0.718033i | ||||
\(202\) | −2552.97 | + | 1819.98i | −0.889238 | + | 0.633929i | ||||
\(203\) | 181.931 | − | 439.221i | 0.0629018 | − | 0.151858i | ||||
\(204\) | −1273.53 | − | 1127.93i | −0.437081 | − | 0.387114i | ||||
\(205\) | 2176.69 | − | 901.616i | 0.741594 | − | 0.307178i | ||||
\(206\) | −1885.96 | + | 434.877i | −0.637869 | + | 0.147084i | ||||
\(207\) | 1749.07i | 0.587288i | ||||||||
\(208\) | −275.265 | + | 988.468i | −0.0917605 | + | 0.329509i | ||||
\(209\) | − | 1724.99i | − | 0.570910i | ||||||
\(210\) | −2322.01 | − | 10070.0i | −0.763018 | − | 3.30903i | ||||
\(211\) | 1661.58 | − | 688.250i | 0.542124 | − | 0.224555i | −0.0947802 | − | 0.995498i | \(-0.530215\pi\) |
0.636904 | + | 0.770943i | \(0.280215\pi\) | |||||||
\(212\) | 746.628 | − | 45.2652i | 0.241880 | − | 0.0146643i | ||||
\(213\) | 2167.10 | − | 5231.85i | 0.697124 | − | 1.68301i | ||||
\(214\) | 2927.84 | + | 4107.01i | 0.935249 | + | 1.31191i | ||||
\(215\) | −666.731 | + | 666.731i | −0.211492 | + | 0.211492i | ||||
\(216\) | 686.296 | + | 373.341i | 0.216188 | + | 0.117605i | ||||
\(217\) | −3596.12 | − | 3596.12i | −1.12498 | − | 1.12498i | ||||
\(218\) | −917.981 | + | 5476.65i | −0.285200 | + | 1.70149i | ||||
\(219\) | −7181.22 | − | 2974.56i | −2.21581 | − | 0.917818i | ||||
\(220\) | 2143.76 | + | 739.438i | 0.656965 | + | 0.226604i | ||||
\(221\) | −170.561 | − | 411.770i | −0.0519147 | − | 0.125333i | ||||
\(222\) | 3747.81 | + | 2343.28i | 1.13305 | + | 0.708427i | ||||
\(223\) | −2657.54 | −0.798035 | −0.399018 | − | 0.916943i | \(-0.630649\pi\) | ||||
−0.399018 | + | 0.916943i | \(0.630649\pi\) | |||||||
\(224\) | 2503.51 | − | 5350.11i | 0.746752 | − | 1.59584i | ||||
\(225\) | −2812.96 | −0.833470 | ||||||||
\(226\) | −3339.16 | − | 2087.78i | −0.982821 | − | 0.614500i | ||||
\(227\) | 833.769 | + | 2012.90i | 0.243785 | + | 0.588549i | 0.997653 | − | 0.0684772i | \(-0.0218140\pi\) |
−0.753868 | + | 0.657026i | \(0.771814\pi\) | |||||||
\(228\) | −1777.45 | + | 5153.14i | −0.516292 | + | 1.49682i | ||||
\(229\) | −5607.23 | − | 2322.59i | −1.61806 | − | 0.670224i | −0.624244 | − | 0.781230i | \(-0.714593\pi\) |
−0.993820 | + | 0.111006i | \(0.964593\pi\) | |||||||
\(230\) | 379.862 | − | 2266.24i | 0.108901 | − | 0.649703i | ||||
\(231\) | 3417.99 | + | 3417.99i | 0.973538 | + | 0.973538i | ||||
\(232\) | −93.3758 | − | 316.162i | −0.0264242 | − | 0.0894700i | ||||
\(233\) | 132.710 | − | 132.710i | 0.0373138 | − | 0.0373138i | −0.688204 | − | 0.725518i | \(-0.741600\pi\) |
0.725518 | + | 0.688204i | \(0.241600\pi\) | |||||||
\(234\) | 829.540 | + | 1163.63i | 0.231747 | + | 0.325081i | ||||
\(235\) | −1218.14 | + | 2940.86i | −0.338140 | + | 0.816343i | ||||
\(236\) | 61.0919 | + | 1007.68i | 0.0168506 | + | 0.277943i | ||||
\(237\) | 6775.83 | − | 2806.64i | 1.85712 | − | 0.769245i | ||||
\(238\) | 576.502 | + | 2500.15i | 0.157013 | + | 0.680928i | ||||
\(239\) | 138.825i | 0.0375727i | 0.999824 | + | 0.0187863i | \(0.00598023\pi\) | ||||
−0.999824 | + | 0.0187863i | \(0.994020\pi\) | |||||||
\(240\) | −5642.22 | − | 4417.91i | −1.51752 | − | 1.18823i | ||||
\(241\) | 4825.11i | 1.28968i | 0.764318 | + | 0.644839i | \(0.223076\pi\) | ||||
−0.764318 | + | 0.644839i | \(0.776924\pi\) | |||||||
\(242\) | 2634.80 | − | 607.549i | 0.699881 | − | 0.161383i | ||||
\(243\) | −5007.97 | + | 2074.37i | −1.32206 | + | 0.547616i | ||||
\(244\) | −2730.72 | + | 3083.19i | −0.716460 | + | 0.808939i | ||||
\(245\) | −4043.20 | + | 9761.15i | −1.05433 | + | 2.54537i | ||||
\(246\) | 2835.65 | − | 2021.51i | 0.734937 | − | 0.523929i | ||||
\(247\) | −1009.83 | + | 1009.83i | −0.260138 | + | 0.260138i | ||||
\(248\) | −3506.94 | − | 371.437i | −0.897948 | − | 0.0951061i | ||||
\(249\) | 7270.88 | + | 7270.88i | 1.85049 | + | 1.85049i | ||||
\(250\) | −1459.28 | − | 244.601i | −0.369172 | − | 0.0618796i | ||||
\(251\) | −3296.58 | − | 1365.49i | −0.828996 | − | 0.343381i | −0.0724909 | − | 0.997369i | \(-0.523095\pi\) |
−0.756505 | + | 0.653988i | \(0.773095\pi\) | |||||||
\(252\) | −3602.37 | − | 7395.99i | −0.900509 | − | 1.84882i | ||||
\(253\) | 411.311 | + | 992.992i | 0.102209 | + | 0.246754i | ||||
\(254\) | 1364.29 | − | 2182.03i | 0.337021 | − | 0.539026i | ||||
\(255\) | 3112.71 | 0.764414 | ||||||||
\(256\) | −982.413 | − | 3976.44i | −0.239847 | − | 0.970811i | ||||
\(257\) | 6601.51 | 1.60230 | 0.801149 | − | 0.598465i | \(-0.204222\pi\) | ||||
0.801149 | + | 0.598465i | \(0.204222\pi\) | |||||||
\(258\) | −738.862 | + | 1181.72i | −0.178293 | + | 0.285158i | ||||
\(259\) | −2551.10 | − | 6158.90i | −0.612038 | − | 1.47759i | ||||
\(260\) | −822.108 | − | 1687.86i | −0.196096 | − | 0.402602i | ||||
\(261\) | −424.180 | − | 175.701i | −0.100598 | − | 0.0416691i | ||||
\(262\) | 2736.89 | + | 458.751i | 0.645366 | + | 0.108174i | ||||
\(263\) | 4812.19 | + | 4812.19i | 1.12826 | + | 1.12826i | 0.990460 | + | 0.137799i | \(0.0440028\pi\) |
0.137799 | + | 0.990460i | \(0.455997\pi\) | |||||||
\(264\) | 3333.23 | + | 353.039i | 0.777069 | + | 0.0823032i | ||||
\(265\) | −967.760 | + | 967.760i | −0.224336 | + | 0.224336i | ||||
\(266\) | 6694.37 | − | 4772.35i | 1.54308 | − | 1.10004i | ||||
\(267\) | 3345.06 | − | 8075.69i | 0.766720 | − | 1.85103i | ||||
\(268\) | 2006.51 | − | 2265.51i | 0.457340 | − | 0.516372i | ||||
\(269\) | 952.102 | − | 394.374i | 0.215802 | − | 0.0893880i | −0.272164 | − | 0.962251i | \(-0.587739\pi\) |
0.487965 | + | 0.872863i | \(0.337739\pi\) | |||||||
\(270\) | −1392.95 | + | 321.195i | −0.313971 | + | 0.0723975i | ||||
\(271\) | − | 134.675i | − | 0.0301880i | −0.999886 | − | 0.0150940i | \(-0.995195\pi\) | ||
0.999886 | − | 0.0150940i | \(-0.00480475\pi\) | |||||||
\(272\) | 1400.83 | + | 1096.87i | 0.312272 | + | 0.244512i | ||||
\(273\) | − | 4001.87i | − | 0.887195i | ||||||
\(274\) | 738.274 | + | 3201.72i | 0.162776 | + | 0.705923i | ||||
\(275\) | −1596.99 | + | 661.496i | −0.350190 | + | 0.145053i | ||||
\(276\) | −205.536 | − | 3390.23i | −0.0448255 | − | 0.739375i | ||||
\(277\) | 196.577 | − | 474.579i | 0.0426396 | − | 0.102941i | −0.901125 | − | 0.433560i | \(-0.857257\pi\) |
0.943764 | + | 0.330619i | \(0.107257\pi\) | |||||||
\(278\) | −2889.15 | − | 4052.73i | −0.623309 | − | 0.874341i | ||||
\(279\) | −3472.97 | + | 3472.97i | −0.745238 | + | 0.745238i | ||||
\(280\) | 3061.29 | + | 10365.2i | 0.653382 | + | 2.21229i | ||||
\(281\) | −5752.69 | − | 5752.69i | −1.22127 | − | 1.22127i | −0.967181 | − | 0.254087i | \(-0.918225\pi\) |
−0.254087 | − | 0.967181i | \(-0.581775\pi\) | |||||||
\(282\) | −777.792 | + | 4640.28i | −0.164244 | + | 0.979875i | ||||
\(283\) | −30.6153 | − | 12.6813i | −0.00643071 | − | 0.00266369i | 0.379466 | − | 0.925206i | \(-0.376108\pi\) |
−0.385896 | + | 0.922542i | \(0.626108\pi\) | |||||||
\(284\) | −1931.15 | + | 5598.75i | −0.403496 | + | 1.16981i | ||||
\(285\) | −3816.84 | − | 9214.66i | −0.793298 | − | 1.91519i | ||||
\(286\) | 744.592 | + | 465.549i | 0.153946 | + | 0.0962535i | ||||
\(287\) | −5252.22 | −1.08024 | ||||||||
\(288\) | −5166.90 | − | 2417.77i | −1.05716 | − | 0.494683i | ||||
\(289\) | 4140.18 | 0.842700 | ||||||||
\(290\) | 511.446 | + | 319.777i | 0.103563 | + | 0.0647515i | ||||
\(291\) | 4096.16 | + | 9889.01i | 0.825159 | + | 1.99211i | ||||
\(292\) | 7684.83 | + | 2650.69i | 1.54014 | + | 0.531233i | ||||
\(293\) | 6083.38 | + | 2519.82i | 1.21295 | + | 0.502421i | 0.895163 | − | 0.445740i | \(-0.147059\pi\) |
0.317790 | + | 0.948161i | \(0.397059\pi\) | |||||||
\(294\) | −2581.61 | + | 15401.8i | −0.512117 | + | 3.05527i | ||||
\(295\) | −1306.13 | − | 1306.13i | −0.257783 | − | 0.257783i | ||||
\(296\) | −4060.69 | − | 2208.99i | −0.797374 | − | 0.433767i | ||||
\(297\) | 472.799 | − | 472.799i | 0.0923722 | − | 0.0923722i | ||||
\(298\) | −1060.18 | − | 1487.15i | −0.206088 | − | 0.289088i | ||||
\(299\) | 340.523 | − | 822.096i | 0.0658628 | − | 0.159007i | ||||
\(300\) | 5452.37 | − | 330.556i | 1.04931 | − | 0.0636156i | ||||
\(301\) | 1941.97 | − | 804.390i | 0.371871 | − | 0.154034i | ||||
\(302\) | −335.870 | − | 1456.59i | −0.0639972 | − | 0.277541i | ||||
\(303\) | − | 8479.30i | − | 1.60767i | ||||||
\(304\) | 1529.37 | − | 5491.92i | 0.288537 | − | 1.03613i | ||||
\(305\) | − | 7535.84i | − | 1.41476i | ||||||
\(306\) | 2414.54 | − | 556.760i | 0.451078 | − | 0.104013i | ||||
\(307\) | −5493.47 | + | 2275.47i | −1.02127 | + | 0.423022i | −0.829553 | − | 0.558428i | \(-0.811405\pi\) |
−0.191714 | + | 0.981451i | \(0.561405\pi\) | |||||||
\(308\) | −3784.41 | − | 3351.77i | −0.700119 | − | 0.620080i | ||||
\(309\) | 2003.11 | − | 4835.94i | 0.368780 | − | 0.890314i | ||||
\(310\) | 5254.14 | − | 3745.62i | 0.962629 | − | 0.686249i | ||||
\(311\) | −640.062 | + | 640.062i | −0.116703 | + | 0.116703i | −0.763047 | − | 0.646344i | \(-0.776297\pi\) |
0.646344 | + | 0.763047i | \(0.276297\pi\) | |||||||
\(312\) | −1744.64 | − | 2157.99i | −0.316574 | − | 0.391577i | ||||
\(313\) | 571.963 | + | 571.963i | 0.103288 | + | 0.103288i | 0.756862 | − | 0.653574i | \(-0.226731\pi\) |
−0.653574 | + | 0.756862i | \(0.726731\pi\) | |||||||
\(314\) | −1360.85 | − | 228.102i | −0.244577 | − | 0.0409953i | ||||
\(315\) | 13906.6 | + | 5760.29i | 2.48745 | + | 1.03034i | ||||
\(316\) | −6895.75 | + | 3358.72i | −1.22758 | + | 0.597920i | ||||
\(317\) | 1686.24 | + | 4070.95i | 0.298766 | + | 0.721284i | 0.999965 | + | 0.00831921i | \(0.00264812\pi\) |
−0.701200 | + | 0.712965i | \(0.747352\pi\) | |||||||
\(318\) | −1072.46 | + | 1715.27i | −0.189121 | + | 0.302477i | ||||
\(319\) | −282.136 | −0.0495191 | ||||||||
\(320\) | 6169.59 | + | 4254.82i | 1.07778 | + | 0.743287i | ||||
\(321\) | −13640.8 | −2.37183 | ||||||||
\(322\) | −2715.69 | + | 4343.42i | −0.469998 | + | 0.751706i | ||||
\(323\) | 947.634 | + | 2287.79i | 0.163244 | + | 0.394106i | ||||
\(324\) | 4220.07 | − | 2055.47i | 0.723606 | − | 0.352448i | ||||
\(325\) | 1322.15 | + | 547.651i | 0.225660 | + | 0.0934715i | ||||
\(326\) | −3615.24 | − | 605.977i | −0.614201 | − | 0.102951i | ||||
\(327\) | −10619.4 | − | 10619.4i | −1.79589 | − | 1.79589i | ||||
\(328\) | −2832.24 | + | 2289.74i | −0.476781 | + | 0.385457i | ||||
\(329\) | 5017.70 | − | 5017.70i | 0.840836 | − | 0.840836i | ||||
\(330\) | −4993.89 | + | 3560.09i | −0.833044 | + | 0.593869i | ||||
\(331\) | −2604.99 | + | 6288.99i | −0.432577 | + | 1.04433i | 0.545877 | + | 0.837866i | \(0.316197\pi\) |
−0.978453 | + | 0.206467i | \(0.933803\pi\) | |||||||
\(332\) | −8050.33 | − | 7130.00i | −1.33078 | − | 1.17864i | ||||
\(333\) | −5948.00 | + | 2463.74i | −0.978823 | + | 0.405442i | ||||
\(334\) | −2512.80 | + | 579.418i | −0.411659 | + | 0.0949232i | ||||
\(335\) | 5537.28i | 0.903086i | ||||||||
\(336\) | 7851.62 | + | 13912.4i | 1.27482 | + | 2.25887i | ||||
\(337\) | 5051.39i | 0.816518i | 0.912866 | + | 0.408259i | \(0.133864\pi\) | ||||
−0.912866 | + | 0.408259i | \(0.866136\pi\) | |||||||
\(338\) | 1232.88 | + | 5346.73i | 0.198403 | + | 0.860425i | ||||
\(339\) | 9839.85 | − | 4075.80i | 1.57648 | − | 0.653000i | ||||
\(340\) | −3249.40 | + | 196.999i | −0.518304 | + | 0.0314228i | ||||
\(341\) | −1154.99 | + | 2788.40i | −0.183421 | + | 0.442817i | ||||
\(342\) | −4608.92 | − | 6465.13i | −0.728719 | − | 1.02220i | ||||
\(343\) | 8740.21 | − | 8740.21i | 1.37588 | − | 1.37588i | ||||
\(344\) | 696.518 | − | 1280.38i | 0.109168 | − | 0.200678i | ||||
\(345\) | 4394.32 | + | 4394.32i | 0.685746 | + | 0.685746i | ||||
\(346\) | 1206.03 | − | 7195.14i | 0.187389 | − | 1.11796i | ||||
\(347\) | 1548.08 | + | 641.238i | 0.239497 | + | 0.0992030i | 0.499204 | − | 0.866485i | \(-0.333626\pi\) |
−0.259707 | + | 0.965688i | \(0.583626\pi\) | |||||||
\(348\) | 842.837 | + | 290.716i | 0.129830 | + | 0.0447817i | ||||
\(349\) | 3012.90 | + | 7273.78i | 0.462111 | + | 1.11563i | 0.967529 | + | 0.252760i | \(0.0813383\pi\) |
−0.505418 | + | 0.862875i | \(0.668662\pi\) | |||||||
\(350\) | −6985.37 | − | 4367.54i | −1.06681 | − | 0.667013i | ||||
\(351\) | −553.564 | −0.0841797 | ||||||||
\(352\) | −3501.95 | − | 157.587i | −0.530268 | − | 0.0238620i | ||||
\(353\) | −3877.72 | −0.584675 | −0.292337 | − | 0.956315i | \(-0.594433\pi\) | ||||
−0.292337 | + | 0.956315i | \(0.594433\pi\) | |||||||
\(354\) | −2315.01 | − | 1447.44i | −0.347574 | − | 0.217317i | ||||
\(355\) | −4146.89 | − | 10011.5i | −0.619983 | − | 1.49677i | ||||
\(356\) | −2980.85 | + | 8642.02i | −0.443778 | + | 1.28659i | ||||
\(357\) | −6410.84 | − | 2655.46i | −0.950414 | − | 0.393674i | ||||
\(358\) | 1611.84 | − | 9616.19i | 0.237956 | − | 1.41964i | ||||
\(359\) | −80.3532 | − | 80.3532i | −0.0118130 | − | 0.0118130i | 0.701176 | − | 0.712989i | \(-0.252659\pi\) |
−0.712989 | + | 0.701176i | \(0.752659\pi\) | |||||||
\(360\) | 10010.3 | − | 2956.46i | 1.46553 | − | 0.432831i | ||||
\(361\) | 760.577 | − | 760.577i | 0.110887 | − | 0.110887i | ||||
\(362\) | 3519.98 | + | 4937.61i | 0.511066 | + | 0.716893i | ||||
\(363\) | −2798.47 | + | 6756.09i | −0.404632 | + | 0.976867i | ||||
\(364\) | 253.272 | + | 4177.61i | 0.0364700 | + | 0.601555i | ||||
\(365\) | −13741.7 | + | 5692.01i | −1.97062 | + | 0.816256i | ||||
\(366\) | −2502.76 | − | 10853.9i | −0.357435 | − | 1.55011i | ||||
\(367\) | − | 2569.61i | − | 0.365484i | −0.983161 | − | 0.182742i | \(-0.941503\pi\) | ||
0.983161 | − | 0.182742i | \(-0.0584973\pi\) | |||||||
\(368\) | 429.124 | + | 3526.09i | 0.0607870 | + | 0.499484i | ||||
\(369\) | 5072.36i | 0.715601i | ||||||||
\(370\) | 8241.81 | − | 1900.45i | 1.15803 | − | 0.267027i | ||||
\(371\) | 2818.77 | − | 1167.57i | 0.394456 | − | 0.163389i | ||||
\(372\) | 6323.56 | − | 7139.79i | 0.881348 | − | 0.995110i | ||||
\(373\) | 3461.88 | − | 8357.71i | 0.480561 | − | 1.16018i | −0.478782 | − | 0.877934i | \(-0.658922\pi\) |
0.959343 | − | 0.282243i | \(-0.0910785\pi\) | |||||||
\(374\) | 1239.87 | − | 883.890i | 0.171423 | − | 0.122206i | ||||
\(375\) | 2829.60 | − | 2829.60i | 0.389652 | − | 0.389652i | ||||
\(376\) | 518.271 | − | 4893.28i | 0.0710845 | − | 0.671148i | ||||
\(377\) | 165.166 | + | 165.166i | 0.0225636 | + | 0.0225636i | ||||
\(378\) | 3142.88 | + | 526.802i | 0.427652 | + | 0.0716819i | ||||
\(379\) | 200.232 | + | 82.9388i | 0.0271378 | + | 0.0112408i | 0.396211 | − | 0.918159i | \(-0.370325\pi\) |
−0.369073 | + | 0.929400i | \(0.620325\pi\) | |||||||
\(380\) | 4567.63 | + | 9377.74i | 0.616617 | + | 1.26597i | ||||
\(381\) | 2663.40 | + | 6430.01i | 0.358136 | + | 0.864618i | ||||
\(382\) | −494.990 | + | 791.679i | −0.0662982 | + | 0.106036i | ||||
\(383\) | −4511.40 | −0.601885 | −0.300942 | − | 0.953642i | \(-0.597301\pi\) | ||||
−0.300942 | + | 0.953642i | \(0.597301\pi\) | |||||||
\(384\) | 10299.1 | + | 4079.21i | 1.36869 | + | 0.542100i | ||||
\(385\) | 9249.73 | 1.22444 | ||||||||
\(386\) | −1371.88 | + | 2194.16i | −0.180899 | + | 0.289326i | ||||
\(387\) | −776.844 | − | 1875.47i | −0.102039 | − | 0.246345i | ||||
\(388\) | −4901.90 | − | 10064.0i | −0.641382 | − | 1.31681i | ||||
\(389\) | 4993.23 | + | 2068.26i | 0.650814 | + | 0.269576i | 0.683567 | − | 0.729887i | \(-0.260428\pi\) |
−0.0327533 | + | 0.999463i | \(0.510428\pi\) | |||||||
\(390\) | 5007.61 | + | 839.362i | 0.650180 | + | 0.108981i | ||||
\(391\) | −1091.01 | − | 1091.01i | −0.141112 | − | 0.141112i | ||||
\(392\) | 1720.22 | − | 16241.5i | 0.221643 | − | 2.09265i | ||||
\(393\) | −5306.93 | + | 5306.93i | −0.681169 | + | 0.681169i | ||||
\(394\) | −102.978 | + | 73.4123i | −0.0131675 | + | 0.00938695i | ||||
\(395\) | 5370.69 | − | 12966.0i | 0.684123 | − | 1.65162i | ||||
\(396\) | −3236.99 | + | 3654.81i | −0.410770 | + | 0.463791i | ||||
\(397\) | −7615.39 | + | 3154.40i | −0.962734 | + | 0.398778i | −0.808003 | − | 0.589179i | \(-0.799451\pi\) |
−0.154732 | + | 0.987957i | \(0.549451\pi\) | |||||||
\(398\) | 11486.5 | − | 2648.63i | 1.44665 | − | 0.333578i | ||||
\(399\) | 22234.4i | 2.78975i | ||||||||
\(400\) | −5670.88 | + | 690.144i | −0.708861 | + | 0.0862680i | ||||
\(401\) | − | 5161.80i | − | 0.642813i | −0.946941 | − | 0.321407i | \(-0.895844\pi\) | ||
0.946941 | − | 0.321407i | \(-0.104156\pi\) | |||||||
\(402\) | 1839.01 | + | 7975.34i | 0.228163 | + | 0.989487i | ||||
\(403\) | 2308.51 | − | 956.218i | 0.285348 | − | 0.118195i | ||||
\(404\) | 536.642 | + | 8851.65i | 0.0660864 | + | 1.09007i | ||||
\(405\) | −3286.76 | + | 7934.94i | −0.403260 | + | 0.973557i | ||||
\(406\) | −780.556 | − | 1094.92i | −0.0954146 | − | 0.133842i | ||||
\(407\) | −2797.46 | + | 2797.46i | −0.340700 | + | 0.340700i | ||||
\(408\) | −4614.68 | + | 1362.91i | −0.559953 | + | 0.165377i | ||||
\(409\) | 554.377 | + | 554.377i | 0.0670225 | + | 0.0670225i | 0.739823 | − | 0.672801i | \(-0.234909\pi\) |
−0.672801 | + | 0.739823i | \(0.734909\pi\) | |||||||
\(410\) | 1101.61 | − | 6572.19i | 0.132695 | − | 0.791652i | ||||
\(411\) | −8209.79 | − | 3400.61i | −0.985302 | − | 0.408125i | ||||
\(412\) | −1785.02 | + | 5175.08i | −0.213450 | + | 0.618829i | ||||
\(413\) | 1575.81 | + | 3804.33i | 0.187749 | + | 0.453266i | ||||
\(414\) | 4194.68 | + | 2622.69i | 0.497965 | + | 0.311348i | ||||
\(415\) | 19676.4 | 2.32741 | ||||||||
\(416\) | 1957.83 | + | 2142.34i | 0.230747 | + | 0.252492i | ||||
\(417\) | 13460.6 | 1.58074 | ||||||||
\(418\) | −4136.95 | − | 2586.59i | −0.484078 | − | 0.302666i | ||||
\(419\) | 1812.51 | + | 4375.80i | 0.211330 | + | 0.510195i | 0.993628 | − | 0.112709i | \(-0.0359528\pi\) |
−0.782298 | + | 0.622904i | \(0.785953\pi\) | |||||||
\(420\) | −27632.1 | − | 9531.02i | −3.21026 | − | 1.10730i | ||||
\(421\) | −4077.46 | − | 1688.94i | −0.472026 | − | 0.195520i | 0.133973 | − | 0.990985i | \(-0.457226\pi\) |
−0.605999 | + | 0.795465i | \(0.707226\pi\) | |||||||
\(422\) | 840.919 | − | 5016.89i | 0.0970030 | − | 0.578717i | ||||
\(423\) | −4845.88 | − | 4845.88i | −0.557008 | − | 0.557008i | ||||
\(424\) | 1011.00 | − | 1858.47i | 0.115798 | − | 0.212866i | ||||
\(425\) | 1754.63 | − | 1754.63i | 0.200264 | − | 0.200264i | ||||
\(426\) | −9297.72 | − | 13042.3i | −1.05746 | − | 1.48334i | ||||
\(427\) | −6428.84 | + | 15520.6i | −0.728602 | + | 1.75900i | ||||
\(428\) | 14239.8 | − | 863.306i | 1.60820 | − | 0.0974988i | ||||
\(429\) | −2194.17 | + | 908.853i | −0.246936 | + | 0.102284i | ||||
\(430\) | 599.233 | + | 2598.73i | 0.0672037 | + | 0.291446i | ||||
\(431\) | − | 17343.8i | − | 1.93833i | −0.246418 | − | 0.969164i | \(-0.579254\pi\) | ||
0.246418 | − | 0.969164i | \(-0.420746\pi\) | |||||||
\(432\) | 1924.45 | − | 1086.09i | 0.214329 | − | 0.120959i | ||||
\(433\) | − | 10223.8i | − | 1.13469i | −0.823479 | − | 0.567347i | \(-0.807970\pi\) | ||
0.823479 | − | 0.567347i | \(-0.192030\pi\) | |||||||
\(434\) | −14016.7 | + | 3232.06i | −1.55028 | + | 0.357474i | ||||
\(435\) | −1507.13 | + | 624.274i | −0.166118 | + | 0.0688084i | ||||
\(436\) | 11757.8 | + | 10413.7i | 1.29151 | + | 1.14386i | ||||
\(437\) | −1891.95 | + | 4567.56i | −0.207103 | + | 0.499991i | ||||
\(438\) | −17901.8 | + | 12762.0i | −1.95293 | + | 1.39222i | ||||
\(439\) | −12436.5 | + | 12436.5i | −1.35208 | + | 1.35208i | −0.468742 | + | 0.883335i | \(0.655293\pi\) |
−0.883335 | + | 0.468742i | \(0.844707\pi\) | |||||||
\(440\) | 4987.87 | − | 4032.48i | 0.540426 | − | 0.436911i | ||||
\(441\) | −16084.2 | − | 16084.2i | −1.73676 | − | 1.73676i | ||||
\(442\) | −1243.28 | − | 208.395i | −0.133793 | − | 0.0224261i | ||||
\(443\) | 9677.23 | + | 4008.44i | 1.03788 | + | 0.429902i | 0.835549 | − | 0.549416i | \(-0.185150\pi\) |
0.202327 | + | 0.979318i | \(0.435150\pi\) | |||||||
\(444\) | 11239.5 | − | 5474.44i | 1.20136 | − | 0.585148i | ||||
\(445\) | −6400.98 | − | 15453.3i | −0.681878 | − | 1.64620i | ||||
\(446\) | −3984.92 | + | 6373.42i | −0.423075 | + | 0.676659i | ||||
\(447\) | 4939.36 | 0.522648 | ||||||||
\(448\) | −9076.90 | − | 14026.4i | −0.957239 | − | 1.47921i | ||||
\(449\) | −2416.16 | −0.253954 | −0.126977 | − | 0.991906i | \(-0.540527\pi\) | ||||
−0.126977 | + | 0.991906i | \(0.540527\pi\) | |||||||
\(450\) | −4217.97 | + | 6746.16i | −0.441860 | + | 0.706704i | ||||
\(451\) | 1192.82 | + | 2879.71i | 0.124540 | + | 0.300666i | ||||
\(452\) | −10014.0 | + | 4877.53i | −1.04208 | + | 0.507566i | ||||
\(453\) | 3734.96 | + | 1547.07i | 0.387381 | + | 0.160458i | ||||
\(454\) | 6077.63 | + | 1018.72i | 0.628276 | + | 0.105310i | ||||
\(455\) | −5414.91 | − | 5414.91i | −0.557922 | − | 0.557922i | ||||
\(456\) | 9693.23 | + | 11989.8i | 0.995454 | + | 1.23130i | ||||
\(457\) | 6285.99 | − | 6285.99i | 0.643427 | − | 0.643427i | −0.307969 | − | 0.951396i | \(-0.599649\pi\) |
0.951396 | + | 0.307969i | \(0.0996493\pi\) | |||||||
\(458\) | −13978.1 | + | 9964.82i | −1.42610 | + | 1.01665i | ||||
\(459\) | −367.320 | + | 886.789i | −0.0373530 | + | 0.0901782i | ||||
\(460\) | −4865.40 | − | 4309.18i | −0.493153 | − | 0.436775i | ||||
\(461\) | 8841.89 | − | 3662.43i | 0.893292 | − | 0.370014i | 0.111655 | − | 0.993747i | \(-0.464385\pi\) |
0.781637 | + | 0.623733i | \(0.214385\pi\) | |||||||
\(462\) | 13322.4 | − | 3071.96i | 1.34159 | − | 0.309352i | ||||
\(463\) | 7744.43i | 0.777353i | 0.921374 | + | 0.388676i | \(0.127068\pi\) | ||||
−0.921374 | + | 0.388676i | \(0.872932\pi\) | |||||||
\(464\) | −898.248 | − | 250.141i | −0.0898709 | − | 0.0250269i | ||||
\(465\) | 17450.9i | 1.74035i | ||||||||
\(466\) | −119.275 | − | 517.266i | −0.0118568 | − | 0.0514204i | ||||
\(467\) | 7032.30 | − | 2912.87i | 0.696822 | − | 0.288633i | −0.00601716 | − | 0.999982i | \(-0.501915\pi\) |
0.702839 | + | 0.711349i | \(0.251915\pi\) | |||||||
\(468\) | 4034.55 | − | 244.599i | 0.398498 | − | 0.0241594i | ||||
\(469\) | 4723.86 | − | 11404.4i | 0.465091 | − | 1.12283i | ||||
\(470\) | 5226.31 | + | 7331.16i | 0.512919 | + | 0.719492i | ||||
\(471\) | 2638.73 | − | 2638.73i | 0.258145 | − | 0.258145i | ||||
\(472\) | 2508.27 | + | 1364.48i | 0.244603 | + | 0.133063i | ||||
\(473\) | −882.070 | − | 882.070i | −0.0857455 | − | 0.0857455i | ||||
\(474\) | 3429.21 | − | 20458.6i | 0.332297 | − | 1.98248i | ||||
\(475\) | −7345.84 | − | 3042.75i | −0.709580 | − | 0.293918i | ||||
\(476\) | 6860.42 | + | 2366.34i | 0.660603 | + | 0.227859i | ||||
\(477\) | −1127.59 | − | 2722.24i | −0.108236 | − | 0.261306i | ||||
\(478\) | 332.937 | + | 208.166i | 0.0318581 | + | 0.0199190i | ||||
\(479\) | −19364.6 | −1.84716 | −0.923580 | − | 0.383405i | \(-0.874751\pi\) | ||||
−0.923580 | + | 0.383405i | \(0.874751\pi\) | |||||||
\(480\) | −19055.6 | + | 6906.85i | −1.81201 | + | 0.656777i | ||||
\(481\) | 3275.34 | 0.310484 | ||||||||
\(482\) | 11571.8 | + | 7235.14i | 1.09353 | + | 0.683717i | ||||
\(483\) | −5301.61 | − | 12799.2i | −0.499444 | − | 1.20577i | ||||
\(484\) | 2493.77 | − | 7229.88i | 0.234201 | − | 0.678990i | ||||
\(485\) | 18923.3 | + | 7838.27i | 1.77167 | + | 0.733850i | ||||
\(486\) | −2534.51 | + | 15120.8i | −0.236559 | + | 1.41130i | ||||
\(487\) | 2799.10 | + | 2799.10i | 0.260450 | + | 0.260450i | 0.825237 | − | 0.564787i | \(-0.191042\pi\) |
−0.564787 | + | 0.825237i | \(0.691042\pi\) | |||||||
\(488\) | 3299.58 | + | 11172.1i | 0.306076 | + | 1.03635i | ||||
\(489\) | 7010.08 | − | 7010.08i | 0.648276 | − | 0.648276i | ||||
\(490\) | 17346.9 | + | 24333.2i | 1.59929 | + | 2.24339i | ||||
\(491\) | −935.299 | + | 2258.01i | −0.0859663 | + | 0.207541i | −0.961016 | − | 0.276491i | \(-0.910828\pi\) |
0.875050 | + | 0.484032i | \(0.160828\pi\) | |||||||
\(492\) | −596.063 | − | 9831.78i | −0.0546191 | − | 0.900917i | ||||
\(493\) | 374.186 | − | 154.993i | 0.0341836 | − | 0.0141593i | ||||
\(494\) | 907.599 | + | 3936.04i | 0.0826616 | + | 0.358484i | ||||
\(495\) | − | 8932.98i | − | 0.811126i | ||||||
\(496\) | −6149.38 | + | 7853.53i | −0.556684 | + | 0.710956i | ||||
\(497\) | 24157.1i | 2.18027i | ||||||||
\(498\) | 28339.8 | − | 6534.79i | 2.55008 | − | 0.588014i | ||||
\(499\) | −552.418 | + | 228.819i | −0.0495583 | + | 0.0205277i | −0.407325 | − | 0.913283i | \(-0.633538\pi\) |
0.357767 | + | 0.933811i | \(0.383538\pi\) | |||||||
\(500\) | −2774.77 | + | 3132.93i | −0.248183 | + | 0.280218i | ||||
\(501\) | 2668.89 | − | 6443.27i | 0.237998 | − | 0.574579i | ||||
\(502\) | −8217.91 | + | 5858.47i | −0.730644 | + | 0.520869i | ||||
\(503\) | −254.724 | + | 254.724i | −0.0225797 | + | 0.0225797i | −0.718307 | − | 0.695727i | \(-0.755082\pi\) |
0.695727 | + | 0.718307i | \(0.255082\pi\) | |||||||
\(504\) | −23139.1 | − | 2450.77i | −2.04503 | − | 0.216599i | ||||
\(505\) | −11473.3 | − | 11473.3i | −1.01100 | − | 1.01100i | ||||
\(506\) | 2998.19 | + | 502.548i | 0.263410 | + | 0.0441521i | ||||
\(507\) | −13710.0 | − | 5678.86i | −1.20095 | − | 0.497450i | ||||
\(508\) | −3187.30 | − | 6543.81i | −0.278373 | − | 0.571525i | ||||
\(509\) | −5370.63 | − | 12965.8i | −0.467680 | − | 1.12908i | −0.965173 | − | 0.261611i | \(-0.915746\pi\) |
0.497494 | − | 0.867468i | \(-0.334254\pi\) | |||||||
\(510\) | 4667.45 | − | 7465.03i | 0.405251 | − | 0.648152i | ||||
\(511\) | 33157.9 | 2.87049 | ||||||||
\(512\) | −11009.6 | − | 3606.53i | −0.950310 | − | 0.311304i | ||||
\(513\) | 3075.60 | 0.264700 | ||||||||
\(514\) | 9898.82 | − | 15832.0i | 0.849452 | − | 1.35860i | ||||
\(515\) | −3833.08 | − | 9253.88i | −0.327972 | − | 0.791796i | ||||
\(516\) | 1726.15 | + | 3543.94i | 0.147267 | + | 0.302351i | ||||
\(517\) | −3890.69 | − | 1611.58i | −0.330972 | − | 0.137093i | ||||
\(518\) | −18595.9 | − | 3116.99i | −1.57733 | − | 0.264387i | ||||
\(519\) | 13951.6 | + | 13951.6i | 1.17998 | + | 1.17998i | ||||
\(520\) | −5280.63 | − | 559.297i | −0.445329 | − | 0.0471669i | ||||
\(521\) | 2418.86 | − | 2418.86i | 0.203402 | − | 0.203402i | −0.598054 | − | 0.801456i | \(-0.704059\pi\) |
0.801456 | + | 0.598054i | \(0.204059\pi\) | |||||||
\(522\) | −1057.42 | + | 753.826i | −0.0886631 | + | 0.0632070i | ||||
\(523\) | −3061.70 | + | 7391.60i | −0.255982 | + | 0.617996i | −0.998665 | − | 0.0516471i | \(-0.983553\pi\) |
0.742683 | + | 0.669643i | \(0.233553\pi\) | |||||||
\(524\) | 5204.11 | − | 5875.84i | 0.433860 | − | 0.489861i | ||||
\(525\) | 20584.5 | − | 8526.38i | 1.71120 | − | 0.708804i | ||||
\(526\) | 18756.6 | − | 4325.01i | 1.55480 | − | 0.358516i | ||||
\(527\) | − | 4332.65i | − | 0.358128i | ||||||
\(528\) | 5844.79 | − | 7464.52i | 0.481746 | − | 0.615249i | ||||
\(529\) | 9086.56i | 0.746820i | ||||||||
\(530\) | 869.787 | + | 3772.06i | 0.0712851 | + | 0.309147i | ||||
\(531\) | 3674.06 | − | 1521.84i | 0.300264 | − | 0.124374i | ||||
\(532\) | −1407.18 | − | 23210.8i | −0.114678 | − | 1.89157i | ||||
\(533\) | 987.531 | − | 2384.11i | 0.0802528 | − | 0.193747i | ||||
\(534\) | −14351.6 | − | 20131.6i | −1.16302 | − | 1.63142i | ||||
\(535\) | −18457.3 | + | 18457.3i | −1.49155 | + | 1.49155i | ||||
\(536\) | −2424.51 | − | 8209.18i | −0.195379 | − | 0.661534i | ||||
\(537\) | 18646.1 | + | 18646.1i | 1.49840 | + | 1.49840i | ||||
\(538\) | 481.854 | − | 2874.73i | 0.0386137 | − | 0.230368i | ||||
\(539\) | −12913.8 | − | 5349.06i | −1.03198 | − | 0.427459i | ||||
\(540\) | −1318.39 | + | 3822.25i | −0.105064 | + | 0.304599i | ||||
\(541\) | 4520.94 | + | 10914.5i | 0.359280 | + | 0.867379i | 0.995402 | + | 0.0957899i | \(0.0305377\pi\) |
−0.636121 | + | 0.771589i | \(0.719462\pi\) | |||||||
\(542\) | −322.984 | − | 201.943i | −0.0255966 | − | 0.0160040i | ||||
\(543\) | −16399.6 | −1.29608 | ||||||||
\(544\) | 4731.07 | − | 1714.81i | 0.372873 | − | 0.135151i | ||||
\(545\) | −28738.1 | −2.25873 | ||||||||
\(546\) | −9597.45 | − | 6000.72i | −0.752258 | − | 0.470343i | ||||
\(547\) | 4726.46 | + | 11410.7i | 0.369450 | + | 0.891930i | 0.993841 | + | 0.110818i | \(0.0353471\pi\) |
−0.624391 | + | 0.781112i | \(0.714653\pi\) | |||||||
\(548\) | 8785.52 | + | 3030.35i | 0.684852 | + | 0.236223i | ||||
\(549\) | 14989.1 | + | 6208.68i | 1.16524 | + | 0.482660i | ||||
\(550\) | −808.229 | + | 4821.87i | −0.0626600 | + | 0.373828i | ||||
\(551\) | −917.662 | − | 917.662i | −0.0709505 | − | 0.0709505i | ||||
\(552\) | −8438.78 | − | 4590.65i | −0.650685 | − | 0.353969i | ||||
\(553\) | −22122.6 | + | 22122.6i | −1.70117 | + | 1.70117i | ||||
\(554\) | −843.392 | − | 1183.06i | −0.0646793 | − | 0.0907283i | ||||
\(555\) | −8753.78 | + | 21133.5i | −0.669509 | + | 1.61634i | ||||
\(556\) | −14051.7 | + | 851.898i | −1.07180 | + | 0.0649793i | ||||
\(557\) | −2303.67 | + | 954.213i | −0.175242 | + | 0.0725876i | −0.468579 | − | 0.883421i | \(-0.655234\pi\) |
0.293337 | + | 0.956009i | \(0.405234\pi\) | |||||||
\(558\) | 3121.38 | + | 13536.7i | 0.236807 | + | 1.02698i | ||||
\(559\) | 1032.75i | 0.0781407i | ||||||||
\(560\) | 29448.7 | + | 8200.76i | 2.22221 | + | 0.618831i | ||||
\(561\) | 4118.04i | 0.309918i | ||||||||
\(562\) | −22422.4 | + | 5170.30i | −1.68297 | + | 0.388071i | ||||
\(563\) | −2533.84 | + | 1049.55i | −0.189677 | + | 0.0785670i | −0.475501 | − | 0.879715i | \(-0.657733\pi\) |
0.285823 | + | 0.958282i | \(0.407733\pi\) | |||||||
\(564\) | 9962.24 | + | 8823.34i | 0.743769 | + | 0.658740i | ||||
\(565\) | 7799.30 | − | 18829.2i | 0.580742 | − | 1.40204i | ||||
\(566\) | −76.3198 | + | 54.4076i | −0.00566778 | + | 0.00404050i | ||||
\(567\) | 13538.6 | − | 13538.6i | 1.00277 | − | 1.00277i | ||||
\(568\) | 10531.4 | + | 13026.6i | 0.777974 | + | 0.962294i | ||||
\(569\) | −10461.9 | − | 10461.9i | −0.770801 | − | 0.770801i | 0.207445 | − | 0.978247i | \(-0.433485\pi\) |
−0.978247 | + | 0.207445i | \(0.933485\pi\) | |||||||
\(570\) | −27822.2 | − | 4663.49i | −2.04447 | − | 0.342688i | ||||
\(571\) | 21510.2 | + | 8909.80i | 1.57648 | + | 0.653001i | 0.987852 | − | 0.155400i | \(-0.0496668\pi\) |
0.588632 | + | 0.808401i | \(0.299667\pi\) | |||||||
\(572\) | 2233.00 | − | 1087.63i | 0.163228 | − | 0.0795036i | ||||
\(573\) | −966.329 | − | 2332.92i | −0.0704519 | − | 0.170086i | ||||
\(574\) | −7875.59 | + | 12596.1i | −0.572685 | + | 0.915942i | ||||
\(575\) | 4954.16 | 0.359309 | ||||||||
\(576\) | −13546.1 | + | 8766.06i | −0.979894 | + | 0.634119i | ||||
\(577\) | 8321.88 | 0.600424 | 0.300212 | − | 0.953873i | \(-0.402943\pi\) | ||||
0.300212 | + | 0.953873i | \(0.402943\pi\) | |||||||
\(578\) | 6208.12 | − | 9929.16i | 0.446754 | − | 0.714531i | ||||
\(579\) | −2678.21 | − | 6465.77i | −0.192232 | − | 0.464090i | ||||
\(580\) | 1533.80 | − | 747.072i | 0.109806 | − | 0.0534836i | ||||
\(581\) | −40524.8 | − | 16785.9i | −2.89372 | − | 1.19862i | ||||
\(582\) | 29858.3 | + | 5004.78i | 2.12658 | + | 0.356451i | ||||
\(583\) | −1280.32 | − | 1280.32i | −0.0909530 | − | 0.0909530i | ||||
\(584\) | 17880.2 | − | 14455.4i | 1.26693 | − | 1.02426i | ||||
\(585\) | −5229.48 | + | 5229.48i | −0.369594 | + | 0.369594i | ||||
\(586\) | 15165.0 | − | 10811.0i | 1.06905 | − | 0.762114i | ||||
\(587\) | 7994.94 | − | 19301.5i | 0.562158 | − | 1.35717i | −0.345880 | − | 0.938279i | \(-0.612419\pi\) |
0.908037 | − | 0.418890i | \(-0.137581\pi\) | |||||||
\(588\) | 33066.1 | + | 29286.0i | 2.31909 | + | 2.05397i | ||||
\(589\) | −12826.1 | + | 5312.74i | −0.897266 | + | 0.371660i | ||||
\(590\) | −5090.94 | + | 1173.90i | −0.355238 | + | 0.0819132i | ||||
\(591\) | − | 342.028i | − | 0.0238057i | ||||||
\(592\) | −11386.6 | + | 6426.17i | −0.790518 | + | 0.446139i | ||||
\(593\) | − | 17757.1i | − | 1.22968i | −0.788654 | − | 0.614838i | \(-0.789222\pi\) | ||
0.788654 | − | 0.614838i | \(-0.210778\pi\) | |||||||
\(594\) | −424.934 | − | 1842.84i | −0.0293523 | − | 0.127294i | ||||
\(595\) | −12267.6 | + | 5081.39i | −0.845245 | + | 0.350112i | ||||
\(596\) | −5156.26 | + | 312.604i | −0.354377 | + | 0.0214845i | ||||
\(597\) | −12200.0 | + | 29453.5i | −0.836371 | + | 2.01918i | ||||
\(598\) | −1460.98 | − | 2049.37i | −0.0999061 | − | 0.140142i | ||||
\(599\) | 17544.2 | − | 17544.2i | 1.19672 | − | 1.19672i | 0.221578 | − | 0.975143i | \(-0.428879\pi\) |
0.975143 | − | 0.221578i | \(-0.0711206\pi\) | |||||||
\(600\) | 7382.97 | − | 13571.8i | 0.502347 | − | 0.923442i | ||||
\(601\) | 16.0607 | + | 16.0607i | 0.00109006 | + | 0.00109006i | 0.707652 | − | 0.706562i | \(-0.249755\pi\) |
−0.706562 | + | 0.707652i | \(0.749755\pi\) | |||||||
\(602\) | 982.820 | − | 5863.48i | 0.0665395 | − | 0.396972i | ||||
\(603\) | −11013.9 | − | 4562.10i | −0.743814 | − | 0.308098i | ||||
\(604\) | −3996.88 | − | 1378.63i | −0.269256 | − | 0.0928734i | ||||
\(605\) | 5355.04 | + | 12928.2i | 0.359857 | + | 0.868771i | ||||
\(606\) | −20335.4 | − | 12714.5i | −1.36315 | − | 0.852298i | ||||
\(607\) | −15461.8 | −1.03390 | −0.516950 | − | 0.856016i | \(-0.672933\pi\) | ||||
−0.516950 | + | 0.856016i | \(0.672933\pi\) | |||||||
\(608\) | −10877.7 | − | 11902.8i | −0.725574 | − | 0.793953i | ||||
\(609\) | 3636.61 | 0.241975 | ||||||||
\(610\) | −18072.8 | − | 11299.8i | −1.19958 | − | 0.750028i | ||||
\(611\) | 1334.22 | + | 3221.10i | 0.0883418 | + | 0.213276i | ||||
\(612\) | 2285.30 | − | 6625.49i | 0.150944 | − | 0.437614i | ||||
\(613\) | 13837.1 | + | 5731.53i | 0.911708 | + | 0.377642i | 0.788710 | − | 0.614765i | \(-0.210749\pi\) |
0.122998 | + | 0.992407i | \(0.460749\pi\) | |||||||
\(614\) | −2780.22 | + | 16586.7i | −0.182737 | + | 1.09020i | ||||
\(615\) | 12743.7 | + | 12743.7i | 0.835571 | + | 0.835571i | ||||
\(616\) | −13713.0 | + | 4050.01i | −0.896935 | + | 0.264902i | ||||
\(617\) | 6349.72 | − | 6349.72i | 0.414312 | − | 0.414312i | −0.468926 | − | 0.883238i | \(-0.655359\pi\) |
0.883238 | + | 0.468926i | \(0.155359\pi\) | |||||||
\(618\) | −8594.13 | − | 12055.3i | −0.559396 | − | 0.784688i | ||||
\(619\) | 7640.34 | − | 18445.4i | 0.496109 | − | 1.19771i | −0.455455 | − | 0.890259i | \(-0.650523\pi\) |
0.951563 | − | 0.307453i | \(-0.0994767\pi\) | |||||||
\(620\) | −1104.44 | − | 18217.2i | −0.0715408 | − | 1.18003i | ||||
\(621\) | −1770.47 | + | 733.353i | −0.114407 | + | 0.0473888i | ||||
\(622\) | 575.264 | + | 2494.78i | 0.0370836 | + | 0.160823i | ||||
\(623\) | 37287.9i | 2.39793i | ||||||||
\(624\) | −7791.44 | + | 948.215i | −0.499851 | + | 0.0608317i | ||||
\(625\) | − | 18815.1i | − | 1.20417i | ||||||
\(626\) | 2229.35 | − | 514.059i | 0.142337 | − | 0.0328210i | ||||
\(627\) | 12190.8 | − | 5049.59i | 0.776480 | − | 0.321628i | ||||
\(628\) | −2587.61 | + | 2921.61i | −0.164421 | + | 0.185645i | ||||
\(629\) | 2173.37 | − | 5246.97i | 0.137771 | − | 0.332608i | ||||
\(630\) | 34667.2 | − | 24713.9i | 2.19234 | − | 1.56290i | ||||
\(631\) | −3471.86 | + | 3471.86i | −0.219037 | + | 0.219037i | −0.808093 | − | 0.589055i | \(-0.799500\pi\) |
0.589055 | + | 0.808093i | \(0.299500\pi\) | |||||||
\(632\) | −2285.01 | + | 21574.0i | −0.143818 | + | 1.35786i | ||||
\(633\) | 9727.94 | + | 9727.94i | 0.610823 | + | 0.610823i | ||||
\(634\) | 12291.6 | + | 2060.28i | 0.769971 | + | 0.129060i | ||||
\(635\) | 12304.2 | + | 5096.58i | 0.768943 | + | 0.318506i | ||||
\(636\) | 2505.51 | + | 5144.03i | 0.156210 | + | 0.320714i | ||||
\(637\) | 4428.48 | + | 10691.3i | 0.275452 | + | 0.664999i | ||||
\(638\) | −423.057 | + | 676.631i | −0.0262523 | + | 0.0419876i | ||||
\(639\) | 23329.8 | 1.44431 | ||||||||
\(640\) | 19455.3 | − | 8416.14i | 1.20162 | − | 0.519808i | ||||
\(641\) | 7666.55 | 0.472403 | 0.236202 | − | 0.971704i | \(-0.424097\pi\) | ||||
0.236202 | + | 0.971704i | \(0.424097\pi\) | |||||||
\(642\) | −20454.1 | + | 32714.0i | −1.25742 | + | 2.01109i | ||||
\(643\) | −3146.10 | − | 7595.36i | −0.192955 | − | 0.465835i | 0.797560 | − | 0.603240i | \(-0.206124\pi\) |
−0.990515 | + | 0.137405i | \(0.956124\pi\) | |||||||
\(644\) | 6344.46 | + | 13025.7i | 0.388209 | + | 0.797028i | ||||
\(645\) | −6663.62 | − | 2760.16i | −0.406790 | − | 0.168498i | ||||
\(646\) | 6907.63 | + | 1157.84i | 0.420708 | + | 0.0705179i | ||||
\(647\) | −10868.8 | − | 10868.8i | −0.660428 | − | 0.660428i | 0.295053 | − | 0.955481i | \(-0.404663\pi\) |
−0.955481 | + | 0.295053i | \(0.904663\pi\) | |||||||
\(648\) | 1398.38 | − | 13202.9i | 0.0847742 | − | 0.800399i | ||||
\(649\) | 1727.98 | − | 1727.98i | 0.104513 | − | 0.104513i | ||||
\(650\) | 3295.93 | − | 2349.64i | 0.198888 | − | 0.141785i | ||||
\(651\) | 14887.4 | − | 35941.3i | 0.896285 | − | 2.16382i | ||||
\(652\) | −6874.26 | + | 7761.57i | −0.412909 | + | 0.466206i | ||||
\(653\) | −2635.05 | + | 1091.47i | −0.157914 | + | 0.0654099i | −0.460240 | − | 0.887794i | \(-0.652237\pi\) |
0.302327 | + | 0.953204i | \(0.402237\pi\) | |||||||
\(654\) | −41391.5 | + | 9544.33i | −2.47483 | + | 0.570662i | ||||
\(655\) | 14361.6i | 0.856721i | ||||||||
\(656\) | 1244.48 | + | 10225.8i | 0.0740680 | + | 0.608614i | ||||
\(657\) | − | 32022.4i | − | 1.90154i | ||||||
\(658\) | −4509.73 | − | 19557.6i | −0.267185 | − | 1.15872i | ||||
\(659\) | −19323.7 | + | 8004.13i | −1.14225 | + | 0.473136i | −0.871928 | − | 0.489633i | \(-0.837131\pi\) |
−0.270323 | + | 0.962770i | \(0.587131\pi\) | |||||||
\(660\) | 1049.73 | + | 17314.8i | 0.0619102 | + | 1.02118i | ||||
\(661\) | 67.1965 | − | 162.227i | 0.00395407 | − | 0.00954598i | −0.921890 | − | 0.387451i | \(-0.873356\pi\) |
0.925844 | + | 0.377905i | \(0.123356\pi\) | |||||||
\(662\) | 11176.4 | + | 15677.6i | 0.656168 | + | 0.920434i | ||||
\(663\) | 2410.76 | − | 2410.76i | 0.141216 | − | 0.141216i | ||||
\(664\) | −29170.8 | + | 8615.34i | −1.70489 | + | 0.503524i | ||||
\(665\) | 30085.2 | + | 30085.2i | 1.75437 | + | 1.75437i | ||||
\(666\) | −3010.25 | + | 17959.1i | −0.175142 | + | 1.04489i | ||||
\(667\) | 747.061 | + | 309.443i | 0.0433678 | + | 0.0179635i | ||||
\(668\) | −2378.30 | + | 6895.12i | −0.137754 | + | 0.399372i | ||||
\(669\) | −7779.43 | − | 18781.2i | −0.449582 | − | 1.08539i | ||||
\(670\) | 13279.7 | + | 8303.04i | 0.765733 | + | 0.478768i | ||||
\(671\) | 9969.74 | 0.573588 | ||||||||
\(672\) | 45138.6 | + | 2031.23i | 2.59116 | + | 0.116602i | ||||
\(673\) | 3444.70 | 0.197301 | 0.0986503 | − | 0.995122i | \(-0.468547\pi\) | ||||
0.0986503 | + | 0.995122i | \(0.468547\pi\) | |||||||
\(674\) | 12114.5 | + | 7574.45i | 0.692331 | + | 0.432874i | ||||
\(675\) | −1179.42 | − | 2847.38i | −0.0672534 | − | 0.162364i | ||||
\(676\) | 14671.4 | + | 5060.55i | 0.834743 | + | 0.287924i | ||||
\(677\) | −4665.73 | − | 1932.61i | −0.264872 | − | 0.109714i | 0.246295 | − | 0.969195i | \(-0.420787\pi\) |
−0.511167 | + | 0.859481i | \(0.670787\pi\) | |||||||
\(678\) | 4979.90 | − | 29709.9i | 0.282082 | − | 1.68290i | ||||
\(679\) | −32286.9 | − | 32286.9i | −1.82483 | − | 1.82483i | ||||
\(680\) | −4399.96 | + | 8088.24i | −0.248133 | + | 0.456132i | ||||
\(681\) | −11784.7 | + | 11784.7i | −0.663131 | + | 0.663131i | ||||
\(682\) | 4955.37 | + | 6951.10i | 0.278227 | + | 0.390281i | ||||
\(683\) | 537.141 | − | 1296.77i | 0.0300924 | − | 0.0726496i | −0.908119 | − | 0.418712i | \(-0.862482\pi\) |
0.938211 | + | 0.346063i | \(0.112482\pi\) | |||||||
\(684\) | −22415.9 | + | 1358.99i | −1.25306 | + | 0.0759683i | ||||
\(685\) | −15710.0 | + | 6507.27i | −0.876272 | + | 0.362964i | ||||
\(686\) | −7855.37 | − | 34066.9i | −0.437200 | − | 1.89603i | ||||
\(687\) | − | 46426.1i | − | 2.57826i | ||||||
\(688\) | −2026.24 | − | 3590.32i | −0.112282 | − | 0.198953i | ||||
\(689\) | 1499.04i | 0.0828864i | ||||||||
\(690\) | 17127.8 | − | 3949.45i | 0.944994 | − | 0.217903i | ||||
\(691\) | 10591.5 | − | 4387.14i | 0.583097 | − | 0.241526i | −0.0715810 | − | 0.997435i | \(-0.522804\pi\) |
0.654678 | + | 0.755908i | \(0.272804\pi\) | |||||||
\(692\) | −15447.3 | − | 13681.3i | −0.848580 | − | 0.751569i | ||||
\(693\) | −7620.73 | + | 18398.1i | −0.417731 | + | 1.00849i | ||||
\(694\) | 3859.16 | − | 2751.16i | 0.211083 | − | 0.150479i | ||||
\(695\) | 18213.4 | − | 18213.4i | 0.994063 | − | 0.994063i | ||||
\(696\) | 1961.02 | − | 1585.40i | 0.106799 | − | 0.0863428i | ||||
\(697\) | −3163.97 | − | 3163.97i | −0.171943 | − | 0.171943i | ||||
\(698\) | 21962.1 | + | 3681.22i | 1.19094 | + | 0.199622i | ||||
\(699\) | 1326.36 | + | 549.398i | 0.0717706 | + | 0.0297284i | ||||
\(700\) | −20948.8 | + | 10203.6i | −1.13113 | + | 0.550941i | ||||
\(701\) | 2339.32 | + | 5647.61i | 0.126041 | + | 0.304290i | 0.974286 | − | 0.225314i | \(-0.0723406\pi\) |
−0.848245 | + | 0.529604i | \(0.822341\pi\) | |||||||
\(702\) | −830.058 | + | 1327.58i | −0.0446275 | + | 0.0713765i | ||||
\(703\) | −18197.8 | −0.976304 | ||||||||
\(704\) | −5629.03 | + | 8162.22i | −0.301352 | + | 0.436968i | ||||
\(705\) | −24349.4 | −1.30078 | ||||||||
\(706\) | −5814.56 | + | 9299.71i | −0.309963 | + | 0.495750i | ||||
\(707\) | 13842.2 | + | 33417.9i | 0.736334 | + | 1.77767i | ||||
\(708\) | −6942.61 | + | 3381.54i | −0.368530 | + | 0.179500i | ||||
\(709\) | 13955.2 | + | 5780.42i | 0.739207 | + | 0.306189i | 0.720329 | − | 0.693632i | \(-0.243991\pi\) |
0.0188776 | + | 0.999822i | \(0.493991\pi\) | |||||||
\(710\) | −30228.1 | − | 5066.76i | −1.59780 | − | 0.267820i | ||||
\(711\) | 21365.0 | + | 21365.0i | 1.12694 | + | 1.12694i | ||||
\(712\) | 16255.9 | + | 20107.3i | 0.855641 | + | 1.05836i | ||||
\(713\) | 6116.56 | − | 6116.56i | 0.321272 | − | 0.321272i | ||||
\(714\) | −15981.4 | + | 11392.9i | −0.837657 | + | 0.597157i | ||||
\(715\) | −1739.15 | + | 4198.68i | −0.0909657 | + | 0.219611i | ||||
\(716\) | −20645.0 | − | 18284.9i | −1.07757 | − | 0.954381i | ||||
\(717\) | −981.100 | + | 406.385i | −0.0511016 | + | 0.0211670i | ||||
\(718\) | −313.194 | + | 72.2185i | −0.0162790 | + | 0.00375372i | ||||
\(719\) | − | 153.579i | − | 0.00796595i | −0.999992 | − | 0.00398298i | \(-0.998732\pi\) | ||
0.999992 | − | 0.00398298i | \(-0.00126782\pi\) | |||||||
\(720\) | 7919.93 | − | 28440.3i | 0.409942 | − | 1.47209i | ||||
\(721\) | 22329.0i | 1.15336i | ||||||||
\(722\) | −683.578 | − | 2964.52i | −0.0352357 | − | 0.152809i | ||||
\(723\) | −34099.7 | + | 14124.6i | −1.75406 | + | 0.726554i | ||||
\(724\) | 17119.7 | − | 1037.90i | 0.878798 | − | 0.0532781i | ||||
\(725\) | −497.666 | + | 1201.47i | −0.0254936 | + | 0.0615469i | ||||
\(726\) | 12006.5 | + | 16842.0i | 0.613778 | + | 0.860972i | ||||
\(727\) | −5550.98 | + | 5550.98i | −0.283184 | + | 0.283184i | −0.834377 | − | 0.551194i | \(-0.814173\pi\) |
0.551194 | + | 0.834377i | \(0.314173\pi\) | |||||||
\(728\) | 10398.7 | + | 5656.82i | 0.529397 | + | 0.287989i | ||||
\(729\) | −18117.5 | − | 18117.5i | −0.920464 | − | 0.920464i | ||||
\(730\) | −6954.62 | + | 41491.0i | −0.352605 | + | 2.10363i | ||||
\(731\) | 1654.43 | + | 685.286i | 0.0837088 | + | 0.0346733i | ||||
\(732\) | −29783.0 | − | 10272.9i | −1.50384 | − | 0.518713i | ||||
\(733\) | −827.485 | − | 1997.73i | −0.0416969 | − | 0.100665i | 0.901659 | − | 0.432448i | \(-0.142350\pi\) |
−0.943356 | + | 0.331782i | \(0.892350\pi\) | |||||||
\(734\) | −6162.54 | − | 3853.08i | −0.309896 | − | 0.193760i | ||||
\(735\) | −80819.2 | −4.05587 | ||||||||
\(736\) | 9099.88 | + | 4258.16i | 0.455742 | + | 0.213258i | ||||
\(737\) | −7325.69 | −0.366140 | ||||||||
\(738\) | 12164.7 | + | 7605.90i | 0.606762 | + | 0.379373i | ||||
\(739\) | −1375.10 | − | 3319.78i | −0.0684489 | − | 0.165250i | 0.885953 | − | 0.463775i | \(-0.153505\pi\) |
−0.954402 | + | 0.298525i | \(0.903505\pi\) | |||||||
\(740\) | 7800.68 | − | 22615.5i | 0.387512 | − | 1.12346i | ||||
\(741\) | −10092.7 | − | 4180.54i | −0.500358 | − | 0.207255i | ||||
\(742\) | 1426.56 | − | 8510.83i | 0.0705806 | − | 0.421082i | ||||
\(743\) | 22288.2 | + | 22288.2i | 1.10051 | + | 1.10051i | 0.994349 | + | 0.106156i | \(0.0338544\pi\) |
0.106156 | + | 0.994349i | \(0.466146\pi\) | |||||||
\(744\) | −7640.90 | − | 25871.4i | −0.376517 | − | 1.27485i | ||||
\(745\) | 6683.41 | − | 6683.41i | 0.328673 | − | 0.328673i | ||||
\(746\) | −14852.8 | − | 20834.6i | −0.728954 | − | 1.02253i | ||||
\(747\) | −16211.1 | + | 39137.1i | −0.794021 | + | 1.91694i | ||||
\(748\) | −260.625 | − | 4298.88i | −0.0127398 | − | 0.210137i | ||||
\(749\) | 53760.1 | − | 22268.2i | 2.62263 | − | 1.08633i | ||||
\(750\) | −2543.13 | − | 11029.0i | −0.123816 | − | 0.536961i | ||||
\(751\) | − | 24467.3i | − | 1.18885i | −0.804151 | − | 0.594424i | \(-0.797380\pi\) | ||
0.804151 | − | 0.594424i | \(-0.202620\pi\) | |||||||
\(752\) | −10958.1 | − | 8580.30i | −0.531385 | − | 0.416079i | ||||
\(753\) | − | 27294.6i | − | 1.32094i | ||||||
\(754\) | 643.771 | − | 148.445i | 0.0310939 | − | 0.00716983i | ||||
\(755\) | 7147.08 | − | 2960.42i | 0.344515 | − | 0.142703i | ||||
\(756\) | 5976.09 | − | 6747.47i | 0.287498 | − | 0.324607i | ||||
\(757\) | 13698.7 | − | 33071.6i | 0.657712 | − | 1.58786i | −0.143616 | − | 0.989633i | \(-0.545873\pi\) |
0.801328 | − | 0.598225i | \(-0.204127\pi\) | |||||||
\(758\) | 499.151 | − | 355.840i | 0.0239182 | − | 0.0170510i | ||||
\(759\) | −5813.59 | + | 5813.59i | −0.278024 | + | 0.278024i | ||||
\(760\) | 29339.1 | + | 3107.45i | 1.40032 | + | 0.148315i | ||||
\(761\) | 23068.9 | + | 23068.9i | 1.09888 | + | 1.09888i | 0.994542 | + | 0.104338i | \(0.0332725\pi\) |
0.104338 | + | 0.994542i | \(0.466728\pi\) | |||||||
\(762\) | 19414.4 | + | 3254.19i | 0.922979 | + | 0.154707i | ||||
\(763\) | 59188.2 | + | 24516.5i | 2.80833 | + | 1.16325i | ||||
\(764\) | 1156.41 | + | 2374.21i | 0.0547611 | + | 0.112429i | ||||
\(765\) | 4907.38 | + | 11847.5i | 0.231930 | + | 0.559929i | ||||
\(766\) | −6764.75 | + | 10819.4i | −0.319087 | + | 0.510342i | ||||
\(767\) | −2023.17 | −0.0952441 | ||||||||
\(768\) | 25226.3 | − | 18583.1i | 1.18525 | − | 0.873126i | ||||
\(769\) | −22615.1 | −1.06050 | −0.530249 | − | 0.847842i | \(-0.677902\pi\) | ||||
−0.530249 | + | 0.847842i | \(0.677902\pi\) | |||||||
\(770\) | 13869.8 | − | 22183.1i | 0.649132 | − | 1.03821i | ||||
\(771\) | 19324.7 | + | 46653.8i | 0.902672 | + | 2.17924i | ||||
\(772\) | 3205.03 | + | 6580.20i | 0.149419 | + | 0.306770i | ||||
\(773\) | −5061.63 | − | 2096.60i | −0.235516 | − | 0.0975541i | 0.261804 | − | 0.965121i | \(-0.415683\pi\) |
−0.497320 | + | 0.867567i | \(0.665683\pi\) | |||||||
\(774\) | −5662.68 | − | 949.164i | −0.262973 | − | 0.0440788i | ||||
\(775\) | 9837.04 | + | 9837.04i | 0.455944 | + | 0.455944i | ||||
\(776\) | −31486.3 | − | 3334.87i | −1.45656 | − | 0.154271i | ||||
\(777\) | 36058.0 | − | 36058.0i | 1.66483 | − | 1.66483i | ||||
\(778\) | 12447.4 | − | 8873.65i | 0.573602 | − | 0.408915i | ||||
\(779\) | −5486.72 | + | 13246.1i | −0.252352 | + | 0.609231i | ||||
\(780\) | 9521.79 | − | 10750.8i | 0.437096 | − | 0.493515i | ||||
\(781\) | 13245.0 | − | 5486.24i | 0.606840 | − | 0.251361i | ||||
\(782\) | −4252.46 | + | 980.560i | −0.194460 | + | 0.0448398i | ||||
\(783\) | − | 503.039i | − | 0.0229593i | ||||||
\(784\) | −36371.6 | − | 28479.3i | −1.65687 | − | 1.29734i | ||||
\(785\) | − | 7140.90i | − | 0.324675i | ||||||
\(786\) | 4769.67 | + | 20684.9i | 0.216449 | + | 0.938686i | ||||
\(787\) | −4514.92 | + | 1870.14i | −0.204497 | + | 0.0847056i | −0.482581 | − | 0.875851i | \(-0.660301\pi\) |
0.278084 | + | 0.960557i | \(0.410301\pi\) | |||||||
\(788\) | 21.6464 | + | 357.048i | 0.000978581 | + | 0.0161412i | ||||
\(789\) | −19921.7 | + | 48095.2i | −0.898899 | + | 2.17013i | ||||
\(790\) | −23042.3 | − | 32322.4i | −1.03773 | − | 1.45567i | ||||
\(791\) | −32126.4 | + | 32126.4i | −1.44410 | + | 1.44410i | ||||
\(792\) | 3911.32 | + | 13243.4i | 0.175483 | + | 0.594171i | ||||
\(793\) | −5836.41 | − | 5836.41i | −0.261358 | − | 0.261358i | ||||
\(794\) | −3854.11 | + | 22993.5i | −0.172264 | + | 1.02772i | ||||
\(795\) | −9672.24 | − | 4006.37i | −0.431496 | − | 0.178731i | ||||
\(796\) | 10871.7 | − | 31519.0i | 0.484092 | − | 1.40347i | ||||
\(797\) | −3175.58 | − | 7666.53i | −0.141135 | − | 0.340731i | 0.837468 | − | 0.546486i | \(-0.184035\pi\) |
−0.978603 | + | 0.205755i | \(0.934035\pi\) | |||||||
\(798\) | 53323.4 | + | 33340.0i | 2.36545 | + | 1.47898i | ||||
\(799\) | 6045.40 | 0.267673 | ||||||||
\(800\) | −6848.24 | + | 14635.0i | −0.302652 | + | 0.646782i | ||||
\(801\) | 36011.0 | 1.58850 | ||||||||
\(802\) | −12379.2 | − | 7740.01i | −0.545045 | − | 0.340785i | ||||
\(803\) | −7530.40 | − | 18180.0i | −0.330936 | − | 0.798951i | ||||
\(804\) | 21884.4 | + | 7548.47i | 0.959952 | + | 0.331112i | ||||
\(805\) | −24492.1 | − | 10145.0i | −1.07234 | − | 0.444178i | ||||
\(806\) | 1168.33 | − | 6970.20i | 0.0510578 | − | 0.304609i | ||||
\(807\) | 5574.19 | + | 5574.19i | 0.243149 | + | 0.243149i | ||||
\(808\) | 22033.1 | + | 11985.9i | 0.959309 | + | 0.521858i | ||||
\(809\) | −24242.4 | + | 24242.4i | −1.05355 | + | 1.05355i | −0.0550636 | + | 0.998483i | \(0.517536\pi\) |
−0.998483 | + | 0.0550636i | \(0.982464\pi\) | |||||||
\(810\) | 14101.5 | + | 19780.7i | 0.611698 | + | 0.858054i | ||||
\(811\) | 8971.75 | − | 21659.7i | 0.388460 | − | 0.937825i | −0.601807 | − | 0.798642i | \(-0.705552\pi\) |
0.990267 | − | 0.139183i | \(-0.0444477\pi\) | |||||||
\(812\) | −3796.30 | + | 230.155i | −0.164069 | + | 0.00994688i | ||||
\(813\) | 951.771 | − | 394.236i | 0.0410579 | − | 0.0170067i | ||||
\(814\) | 2514.25 | + | 10903.7i | 0.108261 | + | 0.469503i | ||||
\(815\) | − | 18970.6i | − | 0.815351i | ||||||
\(816\) | −3651.04 | + | 13110.8i | −0.156632 | + | 0.562462i | ||||
\(817\) | − | 5737.95i | − | 0.245711i | ||||||
\(818\) | 2160.81 | − | 498.254i | 0.0923605 | − | 0.0212971i | ||||
\(819\) | 15231.7 | − | 6309.19i | 0.649866 | − | 0.269183i | ||||
\(820\) | −14109.9 | − | 12496.8i | −0.600899 | − | 0.532204i | ||||
\(821\) | −13914.2 | + | 33592.0i | −0.591486 | + | 1.42797i | 0.290580 | + | 0.956851i | \(0.406152\pi\) |
−0.882067 | + | 0.471124i | \(0.843848\pi\) | |||||||
\(822\) | −20465.9 | + | 14589.9i | −0.868406 | + | 0.619078i | ||||
\(823\) | −16528.3 | + | 16528.3i | −0.700050 | + | 0.700050i | −0.964421 | − | 0.264371i | \(-0.914836\pi\) |
0.264371 | + | 0.964421i | \(0.414836\pi\) | |||||||
\(824\) | 9734.49 | + | 12040.8i | 0.411550 | + | 0.509056i | ||||
\(825\) | −9349.78 | − | 9349.78i | −0.394567 | − | 0.394567i | ||||
\(826\) | 11486.6 | + | 1925.35i | 0.483862 | + | 0.0811036i | ||||
\(827\) | −42195.4 | − | 17477.9i | −1.77422 | − | 0.734905i | −0.993998 | − | 0.109399i | \(-0.965107\pi\) |
−0.780219 | − | 0.625506i | \(-0.784893\pi\) | |||||||
\(828\) | 12579.7 | − | 6127.20i | 0.527988 | − | 0.257168i | ||||
\(829\) | 10495.1 | + | 25337.5i | 0.439699 | + | 1.06153i | 0.976053 | + | 0.217535i | \(0.0698015\pi\) |
−0.536353 | + | 0.843994i | \(0.680198\pi\) | |||||||
\(830\) | 29504.3 | − | 47188.7i | 1.23387 | − | 1.97342i | ||||
\(831\) | 3929.37 | 0.164029 | ||||||||
\(832\) | 8073.57 | − | 1482.96i | 0.336419 | − | 0.0617938i | ||||
\(833\) | 20065.6 | 0.834611 | ||||||||
\(834\) | 20183.8 | − | 32281.7i | 0.838021 | − | 1.34032i | ||||
\(835\) | −5107.09 | − | 12329.6i | −0.211662 | − | 0.510998i | ||||
\(836\) | −12406.5 | + | 6042.86i | −0.513264 | + | 0.249996i | ||||
\(837\) | −4971.63 | − | 2059.31i | −0.205310 | − | 0.0850422i | ||||
\(838\) | 13212.0 | + | 2214.57i | 0.544633 | + | 0.0912899i | ||||
\(839\) | −24243.8 | − | 24243.8i | −0.997605 | − | 0.997605i | 0.00239210 | − | 0.999997i | \(-0.499239\pi\) |
−0.999997 | + | 0.00239210i | \(0.999239\pi\) | |||||||
\(840\) | −64291.4 | + | 51976.9i | −2.64079 | + | 2.13497i | ||||
\(841\) | 17095.5 | − | 17095.5i | 0.700953 | − | 0.700953i | ||||
\(842\) | −10164.5 | + | 7246.20i | −0.416025 | + | 0.296580i | ||||
\(843\) | 23815.2 | − | 57495.0i | 0.973000 | − | 2.34903i | ||||
\(844\) | −10770.8 | − | 9539.45i | −0.439272 | − | 0.389054i | ||||
\(845\) | −26234.9 | + | 10866.9i | −1.06806 | + | 0.442404i | ||||
\(846\) | −18887.9 | + | 4355.29i | −0.767587 | + | 0.176995i | ||||
\(847\) | − | 31194.9i | − | 1.26549i | ||||||
\(848\) | −2941.09 | − | 5211.35i | −0.119101 | − | 0.211036i | ||||
\(849\) | − | 253.485i | − | 0.0102469i | ||||||
\(850\) | −1577.00 | − | 6839.07i | −0.0636360 | − | 0.275974i | ||||
\(851\) | 10475.5 | − | 4339.11i | 0.421971 | − | 0.174786i | ||||
\(852\) | −45220.3 | + | 2741.53i | −1.81834 | + | 0.110239i | ||||
\(853\) | −2422.60 | + | 5848.66i | −0.0972428 | + | 0.234765i | −0.965014 | − | 0.262200i | \(-0.915552\pi\) |
0.867771 | + | 0.496965i | \(0.165552\pi\) | |||||||
\(854\) | 27582.2 | + | 38690.7i | 1.10520 | + | 1.55031i | ||||
\(855\) | 29054.9 | − | 29054.9i | 1.16217 | − | 1.16217i | ||||
\(856\) | 19281.9 | − | 35445.1i | 0.769910 | − | 1.41529i | ||||
\(857\) | 9164.60 | + | 9164.60i | 0.365294 | + | 0.365294i | 0.865758 | − | 0.500464i | \(-0.166837\pi\) |
−0.500464 | + | 0.865758i | \(0.666837\pi\) | |||||||
\(858\) | −1110.46 | + | 6624.95i | −0.0441846 | + | 0.263604i | ||||
\(859\) | −35659.4 | − | 14770.6i | −1.41639 | − | 0.586689i | −0.462442 | − | 0.886650i | \(-0.653027\pi\) |
−0.953952 | + | 0.299960i | \(0.903027\pi\) | |||||||
\(860\) | 7130.92 | + | 2459.64i | 0.282747 | + | 0.0975267i | ||||
\(861\) | −15374.9 | − | 37118.2i | −0.608565 | − | 1.46921i | ||||
\(862\) | −41594.5 | − | 26006.6i | −1.64352 | − | 1.02760i | ||||
\(863\) | −2066.31 | −0.0815043 | −0.0407521 | − | 0.999169i | \(-0.512975\pi\) | ||||
−0.0407521 | + | 0.999169i | \(0.512975\pi\) | |||||||
\(864\) | 280.972 | − | 6243.85i | 0.0110635 | − | 0.245857i | ||||
\(865\) | 37755.7 | 1.48409 | ||||||||
\(866\) | −24519.0 | − | 15330.3i | −0.962114 | − | 0.601553i | ||||
\(867\) | 12119.6 | + | 29259.3i | 0.474744 | + | 1.14613i | ||||
\(868\) | −13266.4 | + | 38461.7i | −0.518770 | + | 1.50401i | ||||
\(869\) | 17153.7 | + | 7105.29i | 0.669619 | + | 0.277365i | ||||
\(870\) | −762.751 | + | 4550.55i | −0.0297238 | + | 0.177331i | ||||
\(871\) | 4288.55 | + | 4288.55i | 0.166834 | + | 0.166834i | ||||
\(872\) | 42605.1 | − | 12583.1i | 1.65458 | − | 0.488665i | ||||
\(873\) | −31181.3 | + | 31181.3i | −1.20885 | + | 1.20885i | ||||
\(874\) | 8117.19 | + | 11386.3i | 0.314151 | + | 0.440672i | ||||
\(875\) | −6532.55 | + | 15771.0i | −0.252389 | + | 0.609321i | ||||
\(876\) | 3763.02 | + | 62069.2i | 0.145138 | + | 2.39398i | ||||
\(877\) | −218.985 | + | 90.7068i | −0.00843172 | + | 0.00349253i | −0.386895 | − | 0.922124i | \(-0.626453\pi\) |
0.378464 | + | 0.925616i | \(0.376453\pi\) | |||||||
\(878\) | 11177.5 | + | 48474.0i | 0.429637 | + | 1.86323i | ||||
\(879\) | 50368.5i | 1.93275i | ||||||||
\(880\) | −2191.66 | − | 18008.7i | −0.0839554 | − | 0.689858i | ||||
\(881\) | 6300.18i | 0.240929i | 0.992718 | + | 0.120464i | \(0.0384384\pi\) | ||||
−0.992718 | + | 0.120464i | \(0.961562\pi\) | |||||||
\(882\) | −62691.6 | + | 14455.9i | −2.39335 | + | 0.551875i | ||||
\(883\) | −16904.8 | + | 7002.21i | −0.644272 | + | 0.266866i | −0.680803 | − | 0.732466i | \(-0.738369\pi\) |
0.0365310 | + | 0.999333i | \(0.488369\pi\) | |||||||
\(884\) | −2364.05 | + | 2669.19i | −0.0899451 | + | 0.101555i | ||||
\(885\) | 5407.18 | − | 13054.1i | 0.205379 | − | 0.495829i | ||||
\(886\) | 24124.0 | − | 17197.8i | 0.914742 | − | 0.652111i | ||||
\(887\) | 8766.03 | − | 8766.03i | 0.331832 | − | 0.331832i | −0.521450 | − | 0.853282i | \(-0.674609\pi\) |
0.853282 | + | 0.521450i | \(0.174609\pi\) | |||||||
\(888\) | 3724.38 | − | 35163.9i | 0.140745 | − | 1.32885i | ||||
\(889\) | −20993.5 | − | 20993.5i | −0.792013 | − | 0.792013i | ||||
\(890\) | −46659.0 | − | 7820.85i | −1.75732 | − | 0.294557i | ||||
\(891\) | −10497.7 | − | 4348.31i | −0.394711 | − | 0.163495i | ||||
\(892\) | 9309.68 | + | 19113.6i | 0.349452 | + | 0.717456i | ||||
\(893\) | −7412.93 | − | 17896.4i | −0.277787 | − | 0.670638i | ||||
\(894\) | 7406.46 | − | 11845.8i | 0.277080 | − | 0.443156i | ||||
\(895\) | 50459.9 | 1.88457 | ||||||||
\(896\) | −47249.3 | + | 736.322i | −1.76170 | + | 0.0274540i | ||||
\(897\) | 6806.70 | 0.253366 | ||||||||
\(898\) | −3622.97 | + | 5794.52i | −0.134633 | + | 0.215329i | ||||
\(899\) | 868.941 | + | 2097.81i | 0.0322367 | + | 0.0778263i | ||||
\(900\) | 9854.15 | + | 20231.4i | 0.364969 | + | 0.749313i | ||||
\(901\) | 2401.40 | + | 994.692i | 0.0887927 | + | 0.0367791i | ||||
\(902\) | 8694.86 | + | 1457.41i | 0.320961 | + | 0.0537987i | ||||
\(903\) | 11369.5 | + | 11369.5i | 0.418995 | + | 0.418995i | ||||
\(904\) | −3318.29 | + | 31329.7i | −0.122085 | + | 1.15267i | ||||
\(905\) | −22190.2 | + | 22190.2i | −0.815056 | + | 0.815056i | ||||
\(906\) | 9310.74 | − | 6637.53i | 0.341422 | − | 0.243396i | ||||
\(907\) | −10784.4 | + | 26035.9i | −0.394808 | + | 0.953150i | 0.594069 | + | 0.804414i | \(0.297521\pi\) |
−0.988877 | + | 0.148736i | \(0.952479\pi\) | |||||||
\(908\) | 11556.4 | − | 13048.1i | 0.422371 | − | 0.476890i | ||||
\(909\) | 32273.5 | − | 13368.1i | 1.17761 | − | 0.487781i | ||||
\(910\) | −21105.8 | + | 4866.72i | −0.768846 | + | 0.177286i | ||||
\(911\) | 39106.7i | 1.42224i | 0.703070 | + | 0.711121i | \(0.251812\pi\) | ||||
−0.703070 | + | 0.711121i | \(0.748188\pi\) | |||||||
\(912\) | 43289.2 | − | 5268.28i | 1.57176 | − | 0.191283i | ||||
\(913\) | 26031.4i | 0.943606i | ||||||||
\(914\) | −5649.61 | − | 24501.0i | −0.204456 | − | 0.886676i | ||||
\(915\) | 53256.9 | − | 22059.7i | 1.92417 | − | 0.797019i | ||||
\(916\) | 2938.24 | + | 48464.8i | 0.105985 | + | 1.74817i | ||||
\(917\) | 12251.9 | − | 29578.6i | 0.441213 | − | 1.06518i | ||||
\(918\) | 1575.95 | + | 2210.64i | 0.0566601 | + | 0.0794794i | ||||
\(919\) | 22104.3 | − | 22104.3i | 0.793422 | − | 0.793422i | −0.188626 | − | 0.982049i | \(-0.560404\pi\) |
0.982049 | + | 0.188626i | \(0.0604035\pi\) | |||||||
\(920\) | −17630.0 | + | 5206.88i | −0.631788 | + | 0.186593i | ||||
\(921\) | −32162.2 | − | 32162.2i | −1.15068 | − | 1.15068i | ||||
\(922\) | 4474.83 | − | 26696.7i | 0.159838 | − | 0.953590i | ||||
\(923\) | −10965.5 | − | 4542.05i | −0.391043 | − | 0.161975i | ||||
\(924\) | 12609.3 | − | 36556.6i | 0.448935 | − | 1.30154i | ||||
\(925\) | 6978.44 | + | 16847.4i | 0.248054 | + | 0.598854i | ||||
\(926\) | 18573.0 | + | 11612.6i | 0.659122 | + | 0.412110i | ||||
\(927\) | 21564.4 | 0.764042 | ||||||||
\(928\) | −1946.80 | + | 1779.13i | −0.0688652 | + | 0.0629342i | ||||
\(929\) | −48663.4 | −1.71862 | −0.859308 | − | 0.511459i | \(-0.829105\pi\) | ||||
−0.859308 | + | 0.511459i | \(0.829105\pi\) | |||||||
\(930\) | 41851.4 | + | 26167.2i | 1.47566 | + | 0.922641i | ||||
\(931\) | −24604.6 | − | 59400.8i | −0.866147 | − | 2.09106i | ||||
\(932\) | −1419.38 | − | 489.580i | −0.0498855 | − | 0.0172068i | ||||
\(933\) | −6397.08 | − | 2649.76i | −0.224470 | − | 0.0929787i | ||||
\(934\) | 3559.01 | − | 21232.9i | 0.124683 | − | 0.743858i | ||||
\(935\) | 5572.10 | + | 5572.10i | 0.194895 | + | 0.194895i | ||||
\(936\) | 5463.11 | − | 10042.6i | 0.190777 | − | 0.350697i | ||||
\(937\) | 16318.9 | − | 16318.9i | 0.568960 | − | 0.568960i | −0.362877 | − | 0.931837i | \(-0.618205\pi\) |
0.931837 | + | 0.362877i | \(0.118205\pi\) | |||||||
\(938\) | −20267.2 | − | 28429.6i | −0.705488 | − | 0.989617i | ||||
\(939\) | −2367.83 | + | 5716.46i | −0.0822911 | + | 0.198668i | ||||
\(940\) | 25418.6 | − | 1541.03i | 0.881984 | − | 0.0534713i | ||||
\(941\) | 16638.7 | − | 6891.96i | 0.576414 | − | 0.238758i | −0.0753798 | − | 0.997155i | \(-0.524017\pi\) |
0.651793 | + | 0.758397i | \(0.274017\pi\) | |||||||
\(942\) | −2371.59 | − | 10285.0i | −0.0820283 | − | 0.355737i | ||||
\(943\) | − | 8933.39i | − | 0.308495i | ||||||
\(944\) | 7033.46 | − | 3969.42i | 0.242500 | − | 0.136858i | ||||
\(945\) | 16491.9i | 0.567707i | ||||||||
\(946\) | −3438.06 | + | 792.771i | −0.118162 | + | 0.0272465i | ||||
\(947\) | −22740.2 | + | 9419.31i | −0.780315 | + | 0.323217i | −0.737043 | − | 0.675846i | \(-0.763778\pi\) |
−0.0432725 | + | 0.999063i | \(0.513778\pi\) | |||||||
\(948\) | −43922.6 | − | 38901.3i | −1.50479 | − | 1.33276i | ||||
\(949\) | −6234.40 | + | 15051.2i | −0.213253 | + | 0.514839i | ||||
\(950\) | −18312.2 | + | 13054.6i | −0.625396 | + | 0.445838i | ||||
\(951\) | −23833.8 | + | 23833.8i | −0.812687 | + | 0.812687i | ||||
\(952\) | 15962.1 | − | 12904.7i | 0.543419 | − | 0.439331i | ||||
\(953\) | 36291.7 | + | 36291.7i | 1.23358 | + | 1.23358i | 0.962578 | + | 0.271005i | \(0.0873560\pi\) |
0.271005 | + | 0.962578i | \(0.412644\pi\) | |||||||
\(954\) | −8219.38 | − | 1377.71i | −0.278944 | − | 0.0467558i | ||||
\(955\) | −4464.20 | − | 1849.13i | −0.151265 | − | 0.0626560i | ||||
\(956\) | 998.463 | − | 486.323i | 0.0337789 | − | 0.0164527i | ||||
\(957\) | −825.900 | − | 1993.90i | −0.0278971 | − | 0.0673496i | ||||
\(958\) | −29036.8 | + | 46440.9i | −0.979264 | + | 1.56622i | ||||
\(959\) | 37907.1 | 1.27642 | ||||||||
\(960\) | −12009.2 | + | 56056.6i | −0.403744 | + | 1.88460i | ||||
\(961\) | −5500.75 | −0.184645 | ||||||||
\(962\) | 4911.30 | − | 7855.05i | 0.164602 | − | 0.263261i | ||||
\(963\) | −21505.6 | − | 51919.1i | −0.719635 | − | 1.73735i | ||||
\(964\) | 34703.3 | − | 16903.0i | 1.15946 | − | 0.564738i | ||||
\(965\) | −12372.7 | − | 5124.92i | −0.412736 | − | 0.170961i | ||||
\(966\) | −38645.3 | − | 6477.62i | −1.28715 | − | 0.215749i | ||||
\(967\) | −7129.16 | − | 7129.16i | −0.237082 | − | 0.237082i | 0.578559 | − | 0.815641i | \(-0.303615\pi\) |
−0.815641 | + | 0.578559i | \(0.803615\pi\) | |||||||
\(968\) | −13599.6 | − | 16821.7i | −0.451559 | − | 0.558544i | ||||
\(969\) | −13394.1 | + | 13394.1i | −0.444047 | + | 0.444047i | ||||
\(970\) | 47173.1 | − | 33629.2i | 1.56148 | − | 1.11316i | ||||
\(971\) | 3934.25 | − | 9498.11i | 0.130027 | − | 0.313912i | −0.845436 | − | 0.534077i | \(-0.820659\pi\) |
0.975463 | + | 0.220164i | \(0.0706594\pi\) | |||||||
\(972\) | 32462.9 | + | 28751.7i | 1.07124 | + | 0.948776i | ||||
\(973\) | −53049.7 | + | 21973.9i | −1.74789 | + | 0.723999i | ||||
\(974\) | 10910.1 | − | 2515.73i | 0.358914 | − | 0.0827609i | ||||
\(975\) | 10947.0i | 0.359573i | ||||||||
\(976\) | 31741.0 | + | 8839.12i | 1.04099 | + | 0.289891i | ||||
\(977\) | − | 16541.9i | − | 0.541682i | −0.962624 | − | 0.270841i | \(-0.912698\pi\) | ||
0.962624 | − | 0.270841i | \(-0.0873018\pi\) | |||||||
\(978\) | −6300.40 | − | 27323.3i | −0.205996 | − | 0.893358i | ||||
\(979\) | 20444.4 | − | 8468.35i | 0.667422 | − | 0.276455i | ||||
\(980\) | 84368.2 | − | 5114.92i | 2.75004 | − | 0.166725i | ||||
\(981\) | 23677.0 | − | 57161.3i | 0.770589 | − | 1.86037i | ||||
\(982\) | 4012.80 | + | 5628.91i | 0.130401 | + | 0.182918i | ||||
\(983\) | 20577.7 | − | 20577.7i | 0.667678 | − | 0.667678i | −0.289500 | − | 0.957178i | \(-0.593489\pi\) |
0.957178 | + | 0.289500i | \(0.0934891\pi\) | |||||||
\(984\) | −24472.8 | − | 13313.1i | −0.792849 | − | 0.431305i | ||||
\(985\) | −462.796 | − | 462.796i | −0.0149705 | − | 0.0149705i | ||||
\(986\) | 189.374 | − | 1129.80i | 0.00611652 | − | 0.0364910i | ||||
\(987\) | 50149.3 | + | 20772.5i | 1.61729 | + | 0.669905i | ||||
\(988\) | 10800.5 | + | 3725.37i | 0.347783 | + | 0.119959i | ||||
\(989\) | 1368.17 | + | 3303.05i | 0.0439891 | + | 0.106199i | ||||
\(990\) | −21423.4 | − | 13394.8i | −0.687759 | − | 0.430015i | ||||
\(991\) | −31319.0 | −1.00392 | −0.501958 | − | 0.864892i | \(-0.667387\pi\) | ||||
−0.501958 | + | 0.864892i | \(0.667387\pi\) | |||||||
\(992\) | 9613.79 | + | 26523.9i | 0.307700 | + | 0.848926i | ||||
\(993\) | −52070.9 | −1.66407 | ||||||||
\(994\) | 57934.5 | + | 36223.0i | 1.84866 | + | 1.15586i | ||||
\(995\) | 23345.5 | + | 56361.1i | 0.743822 | + | 1.79574i | ||||
\(996\) | 26823.0 | − | 77764.6i | 0.853333 | − | 2.47396i | ||||
\(997\) | −12142.4 | − | 5029.56i | −0.385712 | − | 0.159767i | 0.181397 | − | 0.983410i | \(-0.441938\pi\) |
−0.567109 | + | 0.823643i | \(0.691938\pi\) | |||||||
\(998\) | −279.576 | + | 1667.94i | −0.00886755 | + | 0.0529035i | ||||
\(999\) | −4987.78 | − | 4987.78i | −0.157964 | − | 0.157964i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 32.4.g.a.5.8 | ✓ | 44 | |
4.3 | odd | 2 | 128.4.g.a.113.2 | 44 | |||
8.3 | odd | 2 | 256.4.g.a.225.10 | 44 | |||
8.5 | even | 2 | 256.4.g.b.225.2 | 44 | |||
32.3 | odd | 8 | 256.4.g.a.33.10 | 44 | |||
32.13 | even | 8 | inner | 32.4.g.a.13.8 | yes | 44 | |
32.19 | odd | 8 | 128.4.g.a.17.2 | 44 | |||
32.29 | even | 8 | 256.4.g.b.33.2 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.8 | ✓ | 44 | 1.1 | even | 1 | trivial | |
32.4.g.a.13.8 | yes | 44 | 32.13 | even | 8 | inner | |
128.4.g.a.17.2 | 44 | 32.19 | odd | 8 | |||
128.4.g.a.113.2 | 44 | 4.3 | odd | 2 | |||
256.4.g.a.33.10 | 44 | 32.3 | odd | 8 | |||
256.4.g.a.225.10 | 44 | 8.3 | odd | 2 | |||
256.4.g.b.33.2 | 44 | 32.29 | even | 8 | |||
256.4.g.b.225.2 | 44 | 8.5 | even | 2 |